I've caused him trouble.

Literal

I [topic-は] him [to-に] trouble [object-を] placed-[regret-completion-てしまった].

迷惑をかける ('cause trouble, bother, inconvenience') is a set phrase — literally 'hang trouble on someone.' A characteristically Japanese expression reflecting cultural concern about imposing on others. ~てしまう adds the regret/completion sense, common in apology contexts.