While it certainly doesn't seem to be his modus operandi, Steve Rogers seems to tolerate some degree of what we would consider "enhanced interrogation" techniques.
In The Winter Soldier Steve Rogers allows Natasha Romanov to kick Sitwell off a roof with Falcon waiting to catch him and implies he's willing to let her do whatever is necessary to find out Hydra's true purpose.
Jasper Sitwell: Is this little display meant to insinuate that you're gonna throw me off the roof? Because it's really not your style, Rogers.
Steve Rogers: You're right. It's not. It's hers.
[Natasha throws Sitwell off the roof]
Sourced from IMDB
Also in The Winter Soldier Steve has this conversation with Nick Fury regarding Operation Insight:
Nick Fury: You know, I read those SSR files. "Greatest Generation"? You guys did some nasty stuff.
Steve Rogers: Yeah, we compromised. Sometimes in ways that made us not sleep so well. But we did it so that people could be free. This isn't freedom. This is fear.
Nick Fury: S.H.I.E.L.D. takes the world as it is, not as we'd like to be. And it's getting damn near past time for you get with that program, Cap.
Steve Rogers: Don't hold your breath.
Emphasis mine, sourced from IMDB