What is the origin of the phrase, "up for it"?

It looks likely to be of 19th-century origin. There are a couple of references in sense 10e of the second adverbial meaning of up in the OED.

10e. Bound for (a place); ready for (something). Cf. 19a (d).

1870 H. W. Longfellow John Endicott ii, On board the Swallow,..Up for Barbadoes.

1894 R. D. Blackmore Perlycross I. xvi. 243 Christie was quite up for it. She loved a bit of skirmish.

What were you reading that suggested a risqué interpretation? I have never considered that it was, but I can see why it might be thought to be.

The phrase "up for it" has had numerous idiomatic or slang meanings over the past 150 years. The following instances do not represent first occurrences of the phrase in each of the senses represented; instead they are simply examples of the usage.

One early of "the phrase" was "facing charges in a courtroom"—that is, "standing up before a judge to answer for an alleged offense." Thus, for example, from "Local Brevities," in the Los Angeles [California] Herald (May 7, 1875):

Manuel Everisto, desiring to get all he could of our Italian climate, slept in the streets and was arrested. His devotion to nature not being a finable offense cleared him before the Mayor. A Chinaman who took a packing-box off Ducommun's sidewalk was up for it. His devotion to art got him boxed in the city jail.

And from "Sidewalk Notes," in the Dallas [Texas] Herald (February 10, 1882):

A man named Steward raised a rookus Wednesday at the St. George hotel by entering a portion of the premises reserved exclusively for the ladies and was up for it in the mayor's court yesterday.

Another sense of "up for it"—this time "in town for [an occasion]" appears in two early instances from Australia. From an untitled brief item in the [Bega, New South Wales] Southern Star (August 16, 1911):

Big Shire appeal case at Candelo yesterday, Mr. J. M. Black, of Ayrdale, against Imlay Shire. Mr. Rodd, Shire Clerk, was up for it, and several were out from Bega.

And from "Good Times and Being Good," in the Sydney [New South Wales] Stock and Station Journal (July 3, 1914):

Our annual show was held on 13th and 14th of last month. I went and had a great time. Everybody said it was the best show ever held here. A schoolmate of mine was up for it and you may be sure we made the best of our only too-short time. We did have a good time though, and ended up by having a ride on the merry-go-round.

Another Australian usage (from World War I) seems to carry the meaning "in trouble for [something]," and thus has some kinship to the U.S. usage cited earlier in this answer. From "Winter 1916: Coisy, Dernancourt, Flers," in the [Perth, Western Australia] Western Mail (July 28, 1938):

He [the commanding officer, a colonel] espied a digger sitting dejectedly by a collapsed hut, and asked him why he was looking so forlorn. After a few minutes' conversation with the man, the colonel hastened to orderly room, and ordered the officers' call to be sounded on the bugle. The well-known "There's a land of Sunny Skies, Western Australia!" soon broke the silence, followed by the "Officers, come when you're called! Come! Come! Come!" (There are other versions, of course.) As the officers hastened to orderly room, the diggers grinned and audibly suggested that some one was "up for it."

And from "Understanding," in the [Perth, Western Australia] Western Mail (April 11, 1940):

One day a young fellow asked to be paraded to me. I saw him, and he explained that he had gone out walking the previous evening, and that a military policeman had chipped him because he had one of his tunic buttons undone. The lad (he was only nineteen) told the M.P. that he was wasting his time looking for little mistakes like unbuttoned tunics, and that he, the M.P. would be much better employed serving his country in the trenches. The result was that the boy was "up for it," and so he had come to me to see what I could do for him.

Yet another sense of the phrase "up for it" is "in contention or under consideration for [a part or an award]." From Earl Wilson, "It Happened Last Night," in the Indianapolis [Indiana] Times (March 21, 1951):

Gloria Swanson, this year's favorite [for a best actress Oscar], was up for it, too, that first year, for "Sadie Thompson" or was it "Rain"? Glamorous Gloria hopes in '51 to make up for not getting it in '28.

And from "Not Getting Movie Role Lucky Break for Broadway's Eliza," in the San Bernardino [California] Sun (November 6, 1964):

Julie Andrews declares she wasn't terribly upset when the stage role she'd made famous in "My Fair Lady" went to Audrey Hepburn in the movie version.

She declares further she wishes people would quit asking her reaction.

"I knew Audrey was up for it," said Miss Andrews of the Eliza Doolittle role. "I didn't feel badly, I wasn't terribly upset. "I'd already had a crack at the role for three and one-half years on stage."

The earliest newspaper occurrence of "up for it" in the sense of "mentally and physocally prepared for [something]" is from "O'Brien Sets World Shot Record: L.A. Giant Twice Eclipses 60 feet," in the San Bernardino [California] Sun May 9, 1954):

As youngsters and quite a few oldsters swarmed around for his autograph, O'Brien continued to answer questions. He is ordinarily a reticent and retiring young man. > "Yes, I was mentally up. I knew I was up for it. Then Stan Lampert's big mark last week also gave me a lift," O'Brien observed.

And from "Easterbrook Says Bad Breaks, Wind Hurt Nittany Gridders," in the [University Park, Pennsylvania] Daily Collegian (October 25, 1960):

The former Champaign High star connected on 7 of 15 passes for 74 yards and he picked up 29 more on the ground for 103 yard[s] total.

"This was a big win for us. We had lost two in a row and we wanted to get back on the win side. I'm sure glad the whole team was up for it.

The sense of "up for it" in these last two examples is essentially "upbeat, positive, and well prepared"—the opposite of "down-hearted, uninspired, or pessimistic."