Firstly, here is what the ATF (Bureau of Alcohol, Tobacco, and Firearms, which oversees guns and gun ownership in the USA) says:
An alien admitted to the United States under a nonimmigrant visa is prohibited from shipping, transporting, receiving, or possessing a firearm or ammunition unless the alien falls within one of the exceptions provided in 18 U.S.C. 922(y)(2), such as: a valid hunting license or permit, admitted for lawful hunting or sporting purposes, certain official representatives of a foreign government, or a foreign law enforcement officer of a friendly foreign government entering the United States on official law enforcement business.
[18 U.S.C. 922(g)(5)(B) and 922(y)(2); 27 CFR 478.11 and 478.32]
Last Reviewed January 9, 2020
from here: https://www.atf.gov/firearms/qa/may-non ... grant-visa
Secondly, the section this answer refers to:
(2) Exceptions.--Subsections (d)(5)(B), (g)(5)(B), and (s)(3)(B)(v)(II) do not apply to any alien who has been lawfully admitted to the United States under a nonimmigrant visa, if that alien is--
(A) admitted to the United States for lawful hunting or sporting purposes or is in possession of a hunting license or permit lawfully issued in the United States;
(B) an official representative of a foreign government who is--
(i) accredited to the United States Government or the Government's mission to an international organization having its headquarters in the United States; or
(ii) en route to or from another country to which that alien is accredited;
(C) an official of a foreign government or a distinguished foreign visitor who has been so designated by the Department of State; or
(D) a foreign law enforcement officer of a friendly foreign government entering the United States on official law enforcement business.
from here: https://codes.findlaw.com/us/title-18-c ... -sect-922/
Thirdly, any gun that's bought from a FFL (Federal Firearms License) holder will require you to fill out Form 4473. The only way around this would be going to someone's house and buying from them personally, but I'm not sure of the legality of that and you might get into trouble for doing this. If you run afoul of the law, you can guess what might happen to your visa and your job.
Fourthly, when you buy the gun and after you've filled out the form, the dealer is going to call the FBI background check right then and there, before you get the gun. This will take about 10 or 15 minutes, usually. Your name will be checked against records to see whether you are able to have the gun you're buying sold to you.
Fifthly, if you are unfortunate enough to be in a state like New Jersey or any of those states in that part of the country, there are additional laws that will apply. This is also true of Illinois and California. Oregon and Washington have just passed some very prohibative laws, as well. It will be easier in some states to buy a "long gun" (rifle or shotgun) than a handgun. You have to have a firearms purchase license in New Jersey and the gun has to be registered with the local police (but they don't call it registered, because that's against the law!). I knew of a New Jersey state patrol lieutenant who had to register his duty handgun with the local police -- it was the only gun he had! They are very strict in New Jersey and other states, like New York, Maryland, Massachussetts, and Connecticut -- these states are also very strict. You will need to check state laws in the state where you are living.
States like Montana, Idaho, Utah, Wyoming, Arizona, and Texas are much more permissive. If you are living in one of those or some other states, you probably will have less problems.
Sixthly, I don't say that you should not sign and submit a petition, although I don't know who you would submit the petition to and I seriously doubt that it would accomplish anything. Remember that you don't vote, so why would any politician give a hoot about what you think or what your problems are?
Finally, seventhly, I suggest you contact a gun rights group like the NRA (National Rifle Association) and/or GOA (Gun Owners of America) for some help, especially regarding your idea of a petition. They might be more willing to advocate for you regarding the petition, and they might have better information than I can provide to you regarding state laws. There is all kind of legal information about gun ownership online, but finging anything about a Visa holder owning a gun never seems to be a part of that information. Talking to someone who is knowlegable and willing to help may be a good bet.
Remember to be legal. I am guessing that getting entangled with the law over an offense would negatively impact your visa status, as well as your job status, and this might stick with you even after you return home.