Sokolov was selected in the Quebec Major Junior Hockey League (QMJHL) import draft by the Cape Breton Screaming Eagles with the 35th overall pick.[1] After coming over to Canada from Russia for the 2017–18 season his teammate, Drake Batherson, helped get him accustomed to North American life.[2] He played three seasons in the QMJHL with the Screaming Eagles, scoring 97 goals and 191 points in 184 games.[3] In his final season he led the league in goals with 46 and came in third in league scoring with 92 points. He was named to the 2020 QMJHL First All-Star Team and the Screaming Eagles' most valuable player.[4]
He was passed over in two National Hockey League (NHL) entry drafts before being selected by the Ottawa Senators in the second round, 61st overall in the 2020 NHL entry draft.[3] Before his selection by the Senators, Sokolov had attended the development camps of the Columbus Blue Jackets and Toronto Maple Leafs.[5] On November 20, 2020, the Senators signed Sokolov to a three-year entry-level contract.[6] After attending his first training camp, Sokolov was assigned to Ottawa's American Hockey League (AHL) affiliate, the Belleville Senators.[7] He was recalled by the Senators on November 8, 2021[8] and played in his first NHL game on November 9, 2021, against the Boston Bruins.[9] He played the majority of the 2022–23 season with Belleville, scoring 21 goals and 59 points in 70 games.[10] He represented Belleville at the 2023 AHL All-Star Classic.[11] He was recalled late in the NHL season and played in five games with Ottawa.[10] On April 8, 2023, Sokolov scored his first career NHL goal against the Tampa Bay Lightning in a 7-4 win for Ottawa.[12] Sokolov re-signed with Ottawa on September 19, 2023, to a one-year, two-way contract.[10] He failed to make Ottawa's team out of training camp and was placed on waivers. He went unclaimed and was assigned to Belleville to start the 2023–24 season.[13] He spent the entire season in the AHL, playing in 71 games and scoring 21 goals and 46 points, good for second on the team.[14]
After playing his fourth season with the Senators organization, Sokolov was traded to the Utah Hockey Club in exchange for winger Jan Jeník on July 3, 2024.[15] He signed a one-year, two-way contract with Utah on July 9.[14] He was placed on waivers and after going unclaimed, was assigned to Utah's AHL affiliate, the Tucson Roadrunners, to start the 2024–25 season.[16]