As a youth, Platt played in the 1999
Quebec International Pee-Wee Hockey Tournament with a
minor ice hockey team from
North York. Platt played
junior ice hockey in the
Ontario Hockey League for the
North Bay Centennials,
Saginaw Spirit and the
Erie Otters. He has played in the NHL with the
Columbus Blue Jackets and the
Anaheim Ducks. On February 26, 2012, after playing for five years with
Kontinental Hockey League's (KHL)
Dinamo Minsk, Platt accepted Belarusian citizenship. In the
2013–14 season, as leading scorer of Dinamo Minsk in the midst of his 6th season with the club, Platt was traded to
Lokomotiv Yaroslavl for monetary compensation on December 30, 2013. He was later signed to a two-year contract extension with Lokomotiv through to the 2016 season on January 3, 2014. On August 16, 2015, a few days before the start of the new KHL season,
Lokomotiv Yaroslavl broke the contract with him. Lokomotiv's general manager explained this by the uncertain legal status of foreign players in KHL (Lokomotiv had signed 6 foreign players including him while the limit of foreign players for the Russian clubs is only 5 players in the roster) and by Geoff's lack of the Russian passport. Two days later he signed a contract with
CSKA Moscow. Platt left Moscow upon the conclusion of the 2015–16 campaign and took his game to Sweden, signing with the
Växjö Lakers of the
Swedish Hockey League (SHL) on June 23, 2016. On December 14, 2016, he returned to CSKA Moscow for a second stint. On May 7, 2019, Platt signed as a free agent to a two-year contract to continue in the KHL with
Avtomobilist Yekaterinburg. In the midst of his final year under contract with Avtomobilist in the
2020–21, Platt left the club after collecting six points through 28 games and signed for the remainder of the season with
Salavat Yulaev Ufa on December 21, 2020. After the
2022 Russian invasion of Ukraine, he elected to leave the team. As a free agent, Platt opted to continue his career by returning to the Finnish
Liiga and agreed to a one-year contract with
JYP Jyväskylä, on July 11, 2022. However, on December 1, he and JYP Jyväskylä agreed to mutually terminate the contract, and then Platt signed with
Tappara for the rest of the 2022–23 season. ==International play==