Born in Hereford, Herefordshire, Pejic began his career with Wrexham at the age of 14, before training on a Youth Training Scheme and signing a professional contract on 9 August 2002. He made his first-team debut in a 1–1 draw away to Port Vale in April 2001. He broke into the first-team squad in February 2002, making 12 appearances for Wrexham in the remainder of the 2001–02 season. He made 32 appearances in the 2002–03 season, helping Wrexham to promotion to the Second Division and to win the FAW Premier Cup. A hairline fracture of his leg ended his 2003–04 season early after he had made 23 appearances. He signed a new two-year contract in May 2004.