Club career
Early career
Orr joined Kitchee's academy at 11 years old. He enrolled into the IMG Academy three years later in order to further his football education, although he continued to return to Hong Kong every summer to train with Kitchee.
In 2016, Orr chose to play collegiately for San Francisco where he was named to the WCC All-Freshman team. In 2017, he was an integral part of the Dons team that won the West Coast Conference.
In January 2019, he transferred to Syracuse for his senior season.
Kitchee
On 3 July 2019, Kitchee announced an agreement for Orr to join in the second half of the season. On 27 December 2019, Orr returned to Hong Kong, signing a contract with his boyhood club Kitchee.
He made his professional debut on 11 February 2020 in a Sapling Cup match against Rangers. Matthew scored his first Hong Kong Premier League goal in a 2–2 draw against Lee Man on 22 November 2020.
On 20 August 2022, Orr departed Kitchee.
Guangxi Pingguo Haliao
After two years with Kitchee, Orr joined China League One club Guangxi Pingguo Haliao.
On 22 July 2023, Orr became the top scorer in the club's history with 14 goals when he scored a brace in a 2–0 victory against Jiangxi Lushan.
Shanghai Port
On 19 January 2026, Orr joined another CSL club Shanghai Port.
International career
Orr first represented Hong Kong as a 12-year-old with the U13 team. He received his first call up to the U23 squad for the Asian Games.
In 2019, Orr was named to the Hong Kong squad for the 2019 Guangdong–Hong Kong Cup, where he scored a goal in the second leg but was later sent off for violent conduct.
In 2020, Orr was named to the U23 squad that participated in the AFC U-23 Championship Qualifiers held in Ulaanbaatar, Mongolia. Orr started all three games notching an assist.
After an impressive performance during the 2020–21 season of the HKPL, Orr was named in the 25-man squad for the 2022 World Cup qualifying fixtures against Iran, Iraq and Bahrain. He made his international debut against Iran on 3 June 2021, where he also scored his first international goal.
Orr was chosen as one of the over-aged players for the upcoming 2022 Asian Games to be held in Hangzhou, China from 19 September to 17 October 2023. On 27 September, Orr scored the winning goal against Palestine during the Round of 16, in which Hong Kong advanced into the Quarter-Finals for the first time since 1958.
On 26 December 2023, Orr was named in Hong Kong's squad for the 2023 AFC Asian Cup.
