congress does have a sergeant-at-arms position and this position does include powers of arrest. I believe the founders intended the sergeant-at-arms to go after people who are ordered to appear before congress that do not show up. It is a federal crime to fail to appear before congress for a congressional hearing/trial. I do not know if the sergeant-at-arms position is currently filled.
In the world of RealPolitik, he isn't about to arrest anyone.