I was curious so if anyone else wants to know: the last #1 instrumental song on the Billboard Hot 100 chart in the US was "Frankenstein" by The Edgar Winter Group
The most recent was Harlem Shake in 2013. Before that, it was the Miami Vice theme in 1985. Chariots of Fire hit #1 in 1981. Rise by Herb Alpert in 1979. The Star Wars Theme / Cantina Band hit #1 in 1977.
Others can be found https://www.listchallenges.com/instrumental-1-songs. I only validated the ones listed in this post.