Groot is full of mystery, from speaking just only "I'am Groot", to a open story of background and lore, we can't deny that many fans love him for just being mysterious.
But in the movie Avengers: Infinity War, when they are making a new weapon for Thor, Eitri an Asgardian dwarf forge it, but there is a missing part, the handle, so Groot extends his left arm, grab the pieces of the weapon and hold it together, after that he just cut down his arm leaving the axe and a hammer intact to each other to form the Stormbreaker.
So the question is this, how does Groot lift the hammer before cutting his own branch?
The answer is simple, that weapon is not the Mjolnir that only a worthy person can lift. Its another powerful weapon, its the Stormbreaker.
If all of you can remember, Hela, the sister of Thor and Loki, and the villain in the movie Thor Ragnarok, she smashed Mjolnir into pieces, leaving Thor weaponless for the entire movie, until Avengers 2.
Back to Groot, so another question was, does Groot not really worth for Mjolnir? Actually he is, he can wield the Hammer just like Thor.
Just like Vision in the Movie Avengers: Age of Ultron, Vision also can lift Hammer easily.
In the Comics, Groot became a member of Thor Corps who investigates some cases in preserving peace.
Maybe its not the actual Mjolnir, but he had the looks and ability of a Thor.