Is it necessary to seek a divorce in Peru before marrying my current girlfriend?
We cannot give legal advice. The following is not a substitute for the advice of a local attorney. But we hope the information will be useful.
Our information is that there is no need for you to seek a divorce in Peru. In the US, marriage is legally recognized based on state law. If you do not have a state marriage certificate, you are not legally married in the US, so you are free to get married. There might be complications if you were legally married in Peru and you go back to Peru (with your American wife), or if your Peruvian wife comes looking for you in the US. However, if you do not believe these are likely possibilities, you have nothing to worry about.
I mention the following only on the off-chance that it is relevant to you: Peru is largely Catholic. If you had a Catholic wedding there, and you are a practicing Catholic here in the US and want to have a Catholic marriage to your American wife, you will get major flak from the Catholic Church if you are forthright with them - they would consider you outside the good graces of the church and unable to receive the sacraments, unless you were able to get the Peruvian marriage "annulled," which is doubtful, being a matter of Catholic church law for which there must be a recognized reason.
If you are not a practicing Catholic, you can disregard all that.