I am a Russian citizen who was admitted to Ph.D. program in the US university starting this fall. I never before had any US visa and currently waiting for I-20 form from my university. I am become more and more nervous, because political relationship between Russia and US are rather tense now with diplomats deportation and consulates closing. May current situation affect my chances of getting F-1 visa as foreign graduate student?
Assuming that the current climate doesn't degrade into outright war, you should be fine. The most sanctions that US had taken so far against Russian individuals in recent years have been towards very few people in absolute numbers (less than 1000). Beyond such sanctions, it's all speculation, but in a country under the rule of law, it's not like the president or the person in charge of visas in an embassy can just wake up one day and decide to put Russian nationals at the bottom of the pile. The US department of state, which issues visas, and the US department of homeland security, which oversees entry into the country, are both obligated to follow the rule of law; outside of emergency situations, changes need to go through Congress which is usually very slow.
Consider for example that it has been difficult for the current president to use executive orders to enforce a ban on the entry of citizens from some countries that he argued posed a security risk; judges have barred its enforcement multiple times for various reasons.
In other words I wouldn't read too much into the current news cycle in terms of your ability to visit on an F-1 visa.
Diplomatic disputes rarely prevent citizens of any country from obtaining a US F-1 visa (see details on the most recent ban which is subject to a court injunction) but you might face extra delays in the process. Given that you still have 4-5 months before your program starts, you will most likely get the visa in time even if there is a delay. You can mitigate the risk of delays by applying early. Ask your university if they can expedite issuing your I-20 and tell you its SEVIS ID so that you can submit your F-1 visa application right away.