lol, thanks Zach.
There is an old comic that shows that yes, indeed, Captain America is worthy of Mjolnir.
It could also be inferred pretty easily that Cap is worthy simply by looking at his personality and strength of character that he is worthy; Captain America doesn't like bullies, he is a very good leader- able to inspire greatness in people, and the biggest indicator of his strong character comes during the Marvel civil war.
When I say civil war, I don't mean the Confederate army vs. the union; I mean an all-out war between all the superheroes in the United States. Here's a cliff-notes of the story;
A bunch of super-powered teenagers who just want fame decide to do a reality show of them busting villains. The kids bite off more than they can chew when they try to bust some A-lister big bads- one of them being a dude (his name is Nitro) who can make nuclear level explosions radiate out from his body. The big bads quickly find the bumbling kids, it gets violent and Nitro blows the town they're in to kingdom come.
Setting off a nuke in a suburban town is bad enough- the death toll is unimaginable; children, mothers, fathers, that old lady who makes awesome cookies, best friends down the road- nearly everyone dies. This sets off a firestorm when they find out that a bunch of super-powered kids set Nitro off. Every non-powered citizen of America is clamoring for someone to pay, for more oversight and control of the super powered population.
As a result, the government decides to create a mandatory registry of everyone with a super ability. Naturally, it doesn't go over well because EVERYONE has to sign up, including the people who have spent lifetimes being true heroes. Info like that could easily be snatched up by baddies all over the world and put million if not billions of innocent lives in danger. It's also a serious breach of privacy and segregates a whole lot of good people.
Some heroes don't hesitate to put their name down, some find this a violation of their rights and some just don't know. The government starts cracking down on the people who haven't registered and anyone related to them, super or not.
Captain America, even though his name is already registered from decades ago, even though he swore an oath to the government throws that aside because he'd sworn to do something greater, protect good people wherever, whenever. Cap fought against the government crackdown and assembled like-minded heroes who did the same.
As in all wars, it's not the soldiers who suffer the most, it's the innocents caught in the crossfire. When Cap saw this, he gave himself up to government forces in order to put a stop to all the fighting and the suffering.
tldr: Captain America is a true hero and that is why he is worthy of Mjolnir. He also did it in the comics.