Yoda (the sole remaining Jedi Master) sets one very specific precondition on Luke being able to call himself a Jedi, that he has to confront Vader.
“No more training do you require,” Yoda assured him. “Already know you
that which you need.”
“Then I am a Jedi?” Luke pressed. No. He knew he was not, quite.
Something still lacked.
Yoda wrinkled up his wizened features. “Not yet. One thing remains.
Vader … Vader you must confront. Then, only then, a full Jedi you’ll
be. And confront him you will, sooner or later.”
Star Wars Episode VI: Return of the Jedi - Official Novelisation
Since he accomplishes this later in the film, it's fair to say that he's a Jedi.
- Vader thinks Luke is a Jedi.
Vader seemed almost to smile through his mask at his son’s use of Jedi
voice-manipulation. He looked down at the lightsaber the captain had
given him—Luke’s lightsaber. So the boy was truly a Jedi now. A man
grown. He held the lightsaber up. “You have constructed another.”
Star Wars Episode VI: Return of the Jedi - Official Novelisation
He hurled his lightsaber away. “Never! Never will I turn to the dark
side! You have failed, Palpatine. I am a Jedi, as my father was before
me.”
Star Wars Episode VI: Return of the Jedi - Official Novelisation
- The Emperor thinks Luke is a Jedi
The Emperor’s glee turned to a sullen rage. “So be it, Jedi. If you
will not be turned, you will be destroyed.”
Star Wars Episode VI: Return of the Jedi - Official Novelisation
It's also worth noting the film's official novelisation explicitly calls him a Jedi Knight pretty consistently throughout the book.
The monster then turned and started for Luke. But the Jedi Knight
leaped eight meters straight up and grabbed onto the overhead grate.
The crowd began to boo. Hand over hand, Luke traversed the grating
toward the corner of the cave, struggling to maintain his grip as the
audience jeered his efforts. One hand slipped on the oily grid, and he
dangled precariously over the baying mutant.
Star Wars Episode VI: Return of the Jedi - Official Novelisation
The (fully canon) Ultimate Star Wars reference book calls him a Jedi in the timeline on Luke's page.
Jedi Luke Skywalker demands Jabba release Han Solo
The (fully canon) Star Wars in 100 Scenes factbook agrees.
Desperate, the young Jedi [Luke] calls out to his gravely wounded father for
help.
and so does the official StarWars.com Databank article on Luke.
Luke Skywalker was a Tatooine farmboy who rose from humble beginnings
to become one of the greatest Jedi the galaxy has ever known.
Interestingly, the (canon) Star Wars Made Easy: A Beginner's Guide to a Galaxy Far, Far Away factbook pinpoints the precise moment that Luke becomes a fully fledged Jedi, when he casts aside his lightsaber during his duel with Vader.
SO HE IS A JEDI?
No. Luke does call himself a Jedi Knight when he goes to Jabba’s palace, but it is not until later that he truly becomes one by
renouncing the dark side, even though it will likely cost him his
life.