Here's why Captain America is able to wield Stormbreaker in Avengers: Age of Ultron, which suggested Captain America might be worthy enough to wield Thor's powerful hammer, but that wasn't the only weapon belonging to the Asgardian that he used.
Captain America was also shown using weapon capable of killing Thanos, but it also resulted in the Guardians of the Galaxy suggesting that all of them should have something that could kill the Mad Titan. As good of a plan as that might be, Thor said that this wasn't possible since they "simply lack the strength to wield them. Your bodies will crumble as your minds collapse into the madness."
Thor is already widely regarded as one of the MCU's most powerful characters, but this line and his ability to wield Stormbreaker infers that not even someone like Peter Quill (who is Nidavellir weapon without dying. The answer might be two-fold: Captain America is a super-soldier and had the strength to hold Mjolnir before.
If holding Stormbreaker is a matter of simple strength, then Captain America wielding it is all the more impressive. The MCU has shown Captain America's strength in a variety of ways over the years, as he was even able to that part of Steve didn't come from a bottle.
The other aspect of Captain America that could explain his ability to hold Stormbreaker is that he also previously held Mjolnir. Although the creations and enchantments of Thor's weapons are different, the power levels they give the are similar. It is confirmed that one Stormbreaker is the more powerful weapon of the two, after all.
Since Avengers: Endgame concluded with heavily speculated debut of Beta Ray Bill) have a chance to pick up Stormbreaker. If so, then maybe the truth behind Thor's line from Avengers: Infinity War will become more clear.
