Giannini began playing for local side Llanelli Wanderers RFC, and played for Llanelli Schools U15 and Scarlets U16.[2] A captain for the Scarlets U18 side, Giannini made his first appearance for Llanelli RFC in 2021.[3][4]
In 2022, Giannini was selected for Wales U18.[1]
Giannini made his debut for the Scarlets on 24 September 2022 against Ulster. Coming off the bench, Giannini became the second youngest player to represent the Scarlets.[5]
Giannini was selected for Wales U20 in 2023, making his first appearance in a friendly against Poland.[6] He was subsequently named in the full squad for the 2023 Six Nations Under 20s Championship.[7] On 3 February 2022, he made his first appearance, starting against Ireland.[8] He made four appearances during the tournament. Giannini was named in the squad for the 2024 Six Nations Under 20s Championship, and appeared in one match, against France.[9]
Giannini was released by the Scarlets at the end of the 2023–24 United Rugby Championship season.[10] He subsequently joined Swansea RFC ahead of the inaugural Super Rygbi Cymru season.[11]