The 19-year-old joins from Championship high-fliers Norwich City after impressing in their youth set-up.
The English striker has been in fine form for the Canaries' U23 side this season, scoring seven goals in 15 appearances.
Dragons boss Bryan Hughes told the club's official website of his delight at securing the deal.
“Anthony is a highly-rated youngster who has come up through the ranks at Norwich, putting in some very impressive performances along the way," he said.
“We are looking forward to him joining in with the squad and helping us during the last seven games of the season.”
Wrexham currently sit third in the National League behind Solihull Moors and Leyton Orient ahead of a trip to Hartlepool on Saturday.