No. Studies have shown that mosquitoes and other insects do not pass HIV to humans.

When an insect bites a person, it does not inject its own blood or a previous victim’s blood into the new victim. It injects only saliva. Unlike the germs that cause malaria and other diseases spread by insect bites, HIV does not reproduce (and therefore cannot survive) in insects. So, even if the virus enters a mosquito or another sucking or biting insect, the insect does not become infected and cannot pass HIV to the next human that it feeds on or bites.