I would rephrase it as: "He went to London aiming to find a job."

Yes, it is weird. What is aimed? The man, or London? So we have a dangling participle and the sentence needs rewriting. Please ignore the comments which use "for finding". That's completely wrong. I'd write, "He went to London with the aim of finding a job." However, I agree with Rex's and Eamon's suggestions.

He went to London aiming to find a job.

He went to London aimed at finding a job. In this sentence, people might suppose "aimed at finding a job" is used to decorate London. And "aim at" is an action before shooting. The purpose of "he" is planing to find a job. Using for as a collocation is better than "at". Aiming for finding a job,he went to London.

I don't think it is technically incorrect but I think that Rex's rephrasing is much more typical and easier to understand.