The 19-year-old has been a regular fixture in Ronnie Moore's starting XI since joining the League One outfit on New Year's Day.
"Stephen has done well since he has been here," Moore told the club's official website.
"He's only young so he's still learning the game, but he's shown that he's a strong defender who is settling in well to League One football.
"I'd like to thank Fulham for letting Stephen stay with us and hopefully they'll see the benefits when he returns to them in the summer."
Arthurworrey has made six league starts for Tranmere, who have claimed eight points with the teenager in their team.