Sokolov was selected in the
Quebec Major Junior Hockey League (QMJHL) import draft by the
Cape Breton Screaming Eagles with the 35th overall pick. After coming over to Canada from Russia for the 2017–18 season his teammate,
Drake Batherson, helped get him accustomed to North American life. He played three seasons in the QMJHL with the Screaming Eagles, scoring 97 goals and 191 points in 184 games. 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. 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. On November 20, 2020, the Senators signed Sokolov to a three-year entry-level contract. After attending his first training camp, Sokolov was assigned to Ottawa's
American Hockey League (AHL) affiliate, the
Belleville Senators. He was recalled by the Senators on November 8, 2021 and played in his first NHL game on November 9, 2021, against the
Boston Bruins. He played the majority of the
2022–23 season with Belleville, scoring 21 goals and 59 points in 70 games. He represented Belleville at the 2023 AHL All-Star Classic. He was recalled late in the NHL season and played in five games with Ottawa. Sokolov re-signed with Ottawa on September 19, 2023, to a one-year, two-way contract. 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. After playing his fourth season with the Senators organization, Sokolov was traded to
Utah Hockey Club in exchange for winger
Jan Jeník on July 3, 2024. He signed a one-year, two-way contract with Utah on July 9. At the conclusion of his contract with Utah, Sokolov opted to return to his native Russia, signing a one-year contract with
CSKA Moscow of the KHL, after the club acquired his rights from
Avtomobilist Yekaterinburg on 1 July 2025. Before the commencement of the
2025–26 season, Sokolov was traded by CSKA to Torpedo Nizhny Novgorod in exchange for the rights to
Nikolai Kovalenko on 3 July 2025. ==International play==