How can I translate "Jeitinho Brasileiro" into English?

I would say, the Brazilian way, which may furthermore be understood as a Superman reference ("truth, justice, and the American way").

In formal or literary English, the à la <(French) adjective> construction can be used. In this case, you could say, à la brésilienne (no capitals).

I asked a local Brazilian and she said that the phrase is more commonly used to just mean the Brazilian way of doing things:

We put garlic in our rice; it's just the Brazilian Way.

When I mentioned the specific meaning you were aiming for she frowned and took offense. And then offered these suggestions:

Opportunist — unprincipled resourceful person: somebody who takes advantage of something, especially somebody who does so in a devious, unscrupulous, or unprincipled way

Shyster — unethical person: an unscrupulous person, especially a lawyer or political representative

Adding a few of my own:

Circumventing — get around restriction: to find a way of avoiding restrictions imposed by a rule or law without actually breaking it

Loophole — gap in law: a small mistake or omission in a rule or law that allows it to be circumvented

Workaround — way to bypass a problem: a technique that enables somebody to overcome a problem without actually putting things right

To hack the system.

To take advantage of a situation

To find an easier way.

Idiomatic expressions rarely find true equivalents in other languages. So I suggest you take your donkey in, out of the rain. ;)

In case you would be interested in a culturally neutral term (and this sort of behaviour is far from being idiosyncratically Brazilian):

finagler

someone who finagles i.e uses dishonest or devious methods to bring something about

snollygoster - a loanword from a German phrase meaning quick-witted and by extension shrewd and unprincipled (and therefore usually reserved for politicians).

A good metaphor that may apply is monkey business.

monkey business: improper or underhanded conduct; trickery.

I am an American who has lived in Brazil for more than 30 years so I might be qualified to offer an opinion. The phrase "bending the rules" will convey the idea pretty well in situations where creative interpretation of the rules is involved. It does not work in all situations. Brian in Brazil

Being a dual citizen and having lived equally in both countries, I'd like to throw in some thoughts:

• I can relate to @MrHen acquaintance to taking offense to the OPs way of explaining it. It's not about breaking the rules to cheat people out of their hard earned money.
• I also relate to the example of the rice. It can be about doing something that only Brazilians do so.
• "jeitinho" is also used to the same way as "Spit and baling wire"
• I don't believe "jeitinho" and "malandragem" should be associated. The latter implies a harsher degree of breaking the rules.
• Lastly, Wikipedia does a great job of adding context to "jeitinho" which is very important since it carries so much culture with it. I really like this take on it:

savvy, cunning, or sly individuals who use common sense and prior knowledge, as well as naturally gifted intelligence in their thought processes