I am a foreign national currently staying in the United States. Can I apply for a visa in the USA or do I have to do it in my home country?

Citizens of Germany, Latin America, Africa and Asian countries should get their visas in the Russian Consulates on the territory of their native countries. However, if you reside in the US and a have residence permit, work permit, Green Card, etc. you may apply at the Russian Consulate there as well. Before you go to any Russian Consulate you will first need to obtain a visa support invitation.