Warning: mild spoilers for Marvels Snapshots: Civil War #1 by Saladin Ahmed, Ryan Kelly, Rachelle Rosenberg, and VC's Joe Sabino.
The Avengers are some of the strongest, smartest, and otherwise most powerful heroes on Earth, so it can be hard for casual Marvel fans to understand what members like Hawkeye, Black Widow, and Captain America bring to the table. Generally, the answer is that the Avengers face a variety of threats, including many where solutions are found through skill and insight rather than power.
To this end, Steve Rogers is actually one of the most essential Avengers, both binding the team together and using his peerless tactical mind to topple threats as varied as Ultron, Dormammu, and Thanos. And while Captain America is no slouch in combat thanks to his Vibranium-alloy shield and vita-ray-enhanced body, Marvel just dropped another in a long line of hints that his powers may be more varied than they seem.
Marvels Snapshots: Civil War #1 flashes back to Marvel's Civil War event, showing things from the perspective of SHIELD agent Clyde Dobronski and unlicensed hero the Helper. A true believer in the Superhuman Registration Act, Clyde recounts his experiences working as part of a "Cape Killer" enforcement team. Asked to help take down Captain America, he freezes, later explaining, "It was Captain America. His... I dunno, his presence" - an excuse which his superior Maria Hill surprisingly says she understands.
This moment is repeated later from the other side, when the Helper - now captured and being guarded by Clyde - recalls his own experience with Captain America, saying, "When I heard Cap speak, I knew I couldn't just stop. You don't get it. What his voice is like." Throughout Marvel history, there have been many references to the effect meeting Captain America has on a person. In the Daredevil story "Born Again," Steve is even described as having "a voice that could command a god -- and does." So, is there something more than Steve Roger's reputation that makes his voice particularly influential?
What many fans forget is that being bombarded by vita rays turned Steve Rogers into a peak human. This doesn't merely mean it made him more muscular or athletic, but that it enhanced his body to the very limits of human potential. Cap is as fast, strong, and agile as a human can physically be, so why wouldn't he also be more charismatic? While Steve's personality doesn't seem to have been directly altered by the rays, it's reasonable to assume that his reaction times, situational awareness, and even pheromones were.
Steve's body language, tone, and posture are those of an ideal human, and the same heightened reactions that allow him to use his shield as a weapon (something Fallen Son: The Death of Captain America made clear is impossible even for trained SHIELD agents) could just as easily apply to the micro-expressions and body language of those around him. Add to this the fact that Steve's experiences have taken him all around the galaxy, as well as expanding his lifespan, and you have someone perfectly placed to master communication skills alongside combat and tactics.
Captain America's iconic nature explains some of Steve's instant charisma, but it hasn't been shared by people like William Burnside - who took on the mantle - and was shared by the Red Skull when he was reborn in a cloned copy of Steve's body. It would be going too far to suggest that Captain America has a hypnotic voice, but he does seem to be particularly persuasive in a way which would be explained by him using his power set to better read the room, gauging how to approach the people around him just as he'd intuit when a villain was about to reach for their weapon. Steve Rogers is a kind, decent human being, and much of his charisma is simply a personal quality, but it's worth considering how total his physical transformation was, and whether Captain America's ability to instantly win over those around him may be as much to do with his powers as his personality.