WARNING: Major spoilers for Avengers: Endgame.
Captain America goes back in time at the end of Avengers: Endgame and takes Mjolnir with him, but what does he do with Thor's magical hammer? The cherished weapon from Nidavellir that Thor held for years was destroyed in Thor: Ragnarok by Hela, but it makes a return in Avengers: Endgame thanks to the time travel plot.
It is originally Thor who summons Mjolnir when he and Rocket go back to Asgard in the year 2013, during the events of Thor: The Dark World. Their mission was just to obtain the Reality Stone, but Thor couldn't resist getting his trusty hammer back too. He uses both Mjolnir and Stormbreaker during the final battle, but he isn't the only one. Paying off a tease from Avengers: Age of Ultron, Captain America picks up and uses Mjolnir (proving he is worthy) during their fight against Thanos. Cap immediately takes a liking to the hammer, and when he is sent on a mission to put the Infinity Stones back in their proper places in the timeline, he takes Mjolnir with him.
The moment feels natural after how much Captain America has used the hammer already, and since he is about to travel through time all by himself - where he'll possibly meet Red Skull and other threats again - Mjolnir could prove to be useful. But that isn't why Cap takes the weapon with him: it isn't explicitly stated in the movie, but based on Avengers: Endgame's explanation of time travel and branched realities, the most likely reason is that he is also returning Mjolnir to 2013.
Since Thor took the hammer during his trip, this timeline would otherwise be without Mjolnir from 2013 onwards. This would mean he wouldn't be able to stop Malekith in Thor: The Dark World, nor Ultron in Avengers: Age of Ultron. And, considering how vengeful Thor was when forging Stormbreaker, would alter the God of Thunder irreversibly; he may even believe himself not worthy. Mjolnir must be returned to this timeline in order to prevent such a future from playing out; Cap's mission is to "clip all the branches" not just return the Infinity Stones.
This is also just a logical conclusion to make based on how Captain America's story comes to a close in Avengers: Endgame. After putting the six Infinity Stones back, returning Mjolnir, and maybe even making sure Loki remains in custody of the Avengers in 2012, he decides to finally do what makes him happy and spend the rest of his life with Peggy Carter. This future (likely) does not require him to suit up and fight anymore, so he would have no use for Mjolnir either. Simply put, it wouldn't make sense for him to hang on to the hammer if he knew he wasn't going to need it ever again.
Captain America taking Mjolnir back to 2013 helps limit the amount of dangerous realities that Avengers: Endgame potentially created. Sure, he may have used it a few more times in his efforts to return the six Infinity Stones, but then also left it where it belongs. Cap using Mjolnir in Avengers: Endgame fulfilled the fantasies of many, so now he can just sit back and have his dance after restoring the timeline the best he can.
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