Upvote:1
I emailed my local Russian consulate in Houston and the Vice Consul there replied to me that you would need a valid tourist visa on your US Refugee travel document.
Currently (04/28/2021) the Russian consulates in the United States are NOT issuing tourist visas in US travel documents. You may qualify for a different type of visa, as an "emergency situation" due to your refugee status (I do not know your details).
You also may qualify for a Russian tourist visa from your country of origin and can use your old passport to enter with that, if you still have it. If you forfeited your old passport from your home country, you are out of luck.
It is unclear what nationality or country of origin you have, or whether you have a valid passport or any other travel documents that could complicate (or help?) your situation. For instance, if you are from Belarus, and you visit Russia on US refugee travel document, you could be denied re-entry into the USA because the border crossing between Belarus and Russia is minimal, and you could be accused of returning home, and ultimately voiding your refugee travel document.
To re-iterate:
You should contact the Russian Embassy in Washington DC with your missing details provided and see if you meet their requirements.
It is very difficult, but not impossible, to contact them because they are overwhelmed with calls and emails. We had to call them repeatedly (hang up, redial, hang up, redial, etc.) for almost two hours before we finally spoke to a Russian speaking person on the line. They are only open for phone calls two hours a day at our local Russian consulate (Houston). They respond to emails within 24-48 hours.
Also, this similar question was asked a few years ago, and is unanswered, yet relevant.