。
I practiced English with him as a partner.
Literal
I [topic-は] him [object-を] partner do-[sequential-て] English [object-を] practiced.
相手にする ('make into a partner / pair up with, deal with') — 相手 means 'partner, counterpart, opponent.' The を on 彼 marks him as the object being 'made into' a partner. ~にする is the standard 'make X into Y' construction.