Will I test positive for COVID if I get the vaccine?

Short answer: no.

The COVID-19 vaccines will not cause you to test positive on a viral test or rapid antigen test, which is the standard used to diagnose COVID-19 infections. 

Once your body builds an immune response to the virus, you may test positive for an antibody test, and this is actually a good thing.  An antibody test indicates that you may have some level of protection against the virus, either from past infection or through vaccination. Antibody tests are not commonly used to diagnose a current COVID-19 infection.