It depends on the state of the condition. If you have HPV in a benign, undetectable state, then the answer is yes, you can be a surrogate, as it is unlikely to have any effect.
But if a pap test comes up positive, then you won't be accepted, as the infection could be passed on to the baby during delivery. Particularly, when the baby passes through the area that is typically infected, that is when the HPV can be passed along to the child.
Fertility clinics conduct pap tests to confirm that potential surrogates are free from this type of STD. If your pap test is unclean, you won't be eligible to become a surrogate.