If I am going to marry my fiance who has green card, will this affect renewing my F-1 visa?

Marriage will not invalidate your F-1 visa, but I would not advise you to leave the U.S. until you receive a green card because there can be no guarantee that you will be let back in. Every person entering as a non-immigrant must prove, to satisfaction of the U.S. consular or immigration officer, that he/she does not intend to take up residence in the U.S. Being married to an American creates a presumption that you do, in fact, intend to stay in the U.S. (especially if your spouse filed an immigrant petition for you). If your spouse-to-be will remain a permanent resident, you will have to maintain valid status in the U.S. (F-1 or H-1B or any other non-immigrant status) for approximately 2.5 years from the date your spouse would file an immigrant petition for you (currently, it takes about 2 years and 2 months from the petition's date of filing before the beneficiary can apply for a green card, and the waiting period grows steadily). After you will submit your green card application, its processing will take another 6 to 15 months. However, if you spouse becomes a U.S. citizen, rules are more lenient, and the entire process, from the initial filing to the issue of green card, takes 4 to 10 months.

Regardless of your immigration status or lack thereof, you have a right and you can marry in United States in and according to the laws of the state where you choose to marry. It will not negatively impact your chance to get a green card based on that marriage. If your husband is not a US citizen, he must first file the I-130 petition which may not be current immediately. As you await approval of your I-130 petition, it is important for you maintain your F-1 student visa. If CIS determines you violated F-1 status, you may be ineligible to adjust [green card] and may instead have to return to your country to visa process which, may trigger some inadmissibility bars. Please talk to a well recommended immigration attorney.

Since your fiance is a green card holder, you will not be able to adjust status immediately when you get married because you have to wait until your priority date becomes current. Spouses of U.S. citizens do not have to wait for a priority date to become current in order to adjust status. Depending on how long it is before your fiance becomes a citizen, it might be worthwhile to wait until he/she naturalizes. You may also face issues with renewing your student visa if you get married now as the issue of dual intent will come up. There are a lot of things to take into consideration with your situation that cannot be fully answered in a public forum. I suggest you consult with an immigration attorney to discuss the facts specific to your case.