Most things I've seen claim that 気になる is an intransitive verb and that one major difference from 気にする is the transitivity. This includes examples from this site.
However, a native speaker recently mentioned to me that 彼を気になる is fine. Upon further questioning, said native speaker felt that わんこを気になる, パンを気になる, and アメリカを気になる were wrong though. It seems hard to see a pattern here.
I searched shonagon and although there is an overwhelming number of times that が気にな was found (1946), there are still some cases where を気にな was found (16).
Maybe someone can shed some light into when are the kinds of cases that one might use 気になる as a transitive verb.