Yes. Early in S04E07, Conway to a crowd:
You know what I did when 9/11 happened? I joined the Air Force because I wanted to serve my country, just like my grandfather did when he boarded a transport ship on this very dock and sailed to the Pacific to fight the Japanese.
Near the end of the same episode, there is a flashback to the 2013 New Year Party (when Walker was still the President-Elect):
Frank Underwood: So, is it true that you joined up a day after 9/11, or is that just something you say?
Conway: Within 24 hours, honest to God.
Underwood: That's incredible.
Conway: Hey I was 25, just out of law school. You want a career in politics and the Twin Towers fall in your lap? Timing couldn't have been better.
Underwood: How old are you? 35?
If the numbers are all correct, assuming Conway's birthday is between January 1 and September 11, and assuming the usual western/American convention of counting ages, one can conclude that the in-universe 9/11 also took place in 2001.