Saddling a Ghast

I just tried; it is indeed impossible.

You can ride it with Single Player Commands with /saddle. If you jump on it, you will fall through.

Note that Single Player Commands is a mod. It allows for NBT manipulation beyond Vanilla capabilities. Directly riding a Ghast (without intermediate entity) is not possible in Vanilla (unless you count Spectator Mode's mob perspective feature).

While you can't officially ride a ghast, there are cheaty ways to ride pretty much any creature you wish, and ghasts, thanks to their size will keep the (blatantly visible) cheat obscured. Of course the ghast won't be controllable and will fly wherever it wills, it will also happily attack you in survival mode.

The trick is that any mob can have 'passengers' and any mob can be the passenger. - this allows for spider jockeys, chicken jockeys etc. So you can summon a ghast mounted by a saddled pig. Then you can mount the pig, and you're "riding a ghast":

/summon minecraft:ghast ~ ~ ~ {Passengers:[{id:"minecraft:pig",Saddle:1b}]}

Summoning the ghast with:

/summon minecraft:ghast ~ ~ ~ {Passengers:[{id:"minecraft:pig",Saddle:1b,Silent:1b,ActiveEffects:[{Id:14,Amplifier:0,Duration:2147483647}]}]}`

makes the cheat somewhat less blatant, as the pig becomes invisible and silent. The ghast is still completely uncontrollable and hostile though.