Thanks to the super-soldier serum, Steve Rogers has greatly increased physical abilities, often described as being at the peak of human potential. Going along with this is usually the statement that he doesn't have superpowers or superhuman abilities. Both Wikipedia and the Marvel Wikia say that Captain America has "no superhuman powers". His official Marvel Power Grid gives him a strength rating of 3 ("peak human") and a speed rating of 2 ("normal"), both one point below "superhuman", which is consistent with this description.
His actions, however, seem to contradict this.
For example, he can run a mile in 73 seconds (1:13). That's about three times faster than the current world record, and even outpaces a champion thoroughbred. If the rules allowed it, Captain America could win the Kentucy Derby without a horse.
His strength is a little harder to measure. Wikipedia says that he can bench-press 1200 pounds, which again surpasses the world record, but not by nearly as much. His MCU incarnation is shown, in The Avengers, punching a heavy bag off its hanger and across the room, and replacing it with no visible effort. He is also able to pry open a door on the Helicarrier with his bare hands. In Agents of Shield, Mike Peterson pushes a bulldozer across a football field, and is told that he didn't do it as fast as Captain America.
Steve Rogers is said to be at peak human potential and not superhuman, but he is shown doing things that no ordinary human could do, no matter how much they trained. So, is he super-human or not?