On 30th June 2018, it was announced that Josh Giurgi had signed a contract to be an Academy Scholar, playing for the Under-18s. He was previously with Irish side Leixlip United. whom he joined as an Under-10 and who scored over 50 goals for them in all competitions including in an All Ireland semi-final.

He was called up to the Republic of Ireland Under-18s in September 2019 for a tournament in Sweden. His parents are both Romanian.

On 16th July it was announced that Giurgi had signed a professional contract until the end of the 2020/21 season. He signed a further one year contract in July 2021.

He was released by Norwich on 20th May 2022.

On 19th July 2022 it was reported that Irish side Shelbourne had signed Giurgi until the end of the 2022 season. "Josh came in and trained brilliantly last week and thoroughly deserves this deal,” said Shelbourne head coach Damien Duff. “He has great quality on the ball, is very athletic and penetrates brilliantly. He is eager to rebuild his career after leaving Norwich and I am sure we can help him.”

Giurgi added, “I’m delighted to sign for this great club. The players, all of the staff and Gaffer have all been very welcoming from the start and I can’t wait to get on the pitch.”

He switched to Longford Town on 1st January 2023.