Malcom was drafted by Buffalo with the 11^th selection in thee 2015 NLL Entry Draft and was acquired by PCLC via trade with the Albany Firewolves. In Albany, Malcom transitioned from an offensive role into the transition role he plays now. During the 2021-2022 season, he scored 17 points while playing transition for Albany.

Malcom played Jr. A for the New Westminster Salmonbellies, where he contributed 177 points in 48 career games. He played in the NCAA for Mars Hill University, where he was named an All-American (Honorable Mention) by Inside Lacrosse magazine in 2015.

Anthony is the brother of Will Malcom, who also competes for PCLC.