I have an STI and use a condom. Do I still have to tell my partner?

Absolutely!

1. First of all telling your partner is a matter of honesty. If you are even slightly interested in building a decent relationship, with your partner, honesty is a basic ingredient: without it there is no future. 
2. Second, even though wearing a condom will strongly reduce the risk of passing the infection to your partner, the risk will not be gone entirely. In fact certain STIs such as HPV and Herpes, can be passed even when a condom is worn. That’s because sometimes infected area is outside the part covered by the condom. 
3. Third, even in cases where the proper use of a condom totally eliminates the risk of passing the disease, there is always the risk that the condom will break. 

Therefore, even if you use a condom, you could still be exposing your partner(s) to the disease and this is something they have a right to know.