He played seven seasons in Major League Baseball (MLB) from 1943 to 1949 for the Brooklyn Dodgers, Philadelphia Athletics, and Cleveland Indians.

[2] The Brewers signed Peck, and sent him to play for the Hopkinsville Hoppers of the Kentucky–Illinois–Tennessee League in 1938, where he finished the season with a .331 batting average and 16 triples in 130 games.

[4] In one game during the 1940 season against the Columbus Red Birds, Peck chased down a fly ball and ran into an iron fence, knocking himself out.

This cost him his third and fourth toes on his right foot, and ended the White Sox attempt to purchase Peck.

[5][4] Shortly after the accident, the Brooklyn Dodgers purchased Peck from the Brewers and gave him a brief trial in 1943, appearing in one game for the team on May 13.

[5] However, he missed the majority of the season recovering from his foot injury, only playing in 23 games, as it had not yet healed from the offseason and required further surgery.

[6] After playing in two games in 1944, Peck entered the 1945 Philadelphia Athletics season as the team's everyday right fielder after winning the job in spring training.

[8] The Athletics finished the season with 52 wins, and Peck ended his 112 games played with a .276 batting average and nine triples.

[16] In 114 games for the Indians, the highest of his career, he finished the season with a .293 batting average, eight home runs, and 44 RBIs.

[9] Peck entered the 1948 season in a crowded battle for the right field position with the acquisitions of Allie Clark and Thurman Tucker during the offseason.

[18] After he recovered in July, he was originally planned to be sent to the San Diego Padres of the Pacific Coast League, but he was placed back on the Indians' main roster for the rest of the season.

[20] After retirement, Peck lived in Wisconsin for a time with his family, working for Atlantic Richfield Company, then moved to Arizona.