。
She applied for a visa.
Literal
She [topic-は] visa [object-を] applied-for.
申請する is the formal verb for applying — to a government office, school, agency, anywhere with paperwork. It's distinct from 応募する ('apply for a job, contest, position'): 申請 is for permits and entitlements, 応募 is for opportunities one might be selected for. ビザ is a routine English borrowing for travel/residence visas; the more formal Sino-Japanese 査証 also exists but appears mostly in legal documents.