Antibody tests ("Rapid" tests) — give a positive result based on antibodies to HIV, not the virus itself. It takes your body up to 3 months to produce these antibodies at levels that can be detected by this test.
4-6 weeks (up to 3 months) after infection, most people will have enough antibodies to test positive
12 weeks (3 months) after infection, about 98% of people will have enough antibodies to test positive.