Left-back who joined on loan from fellow National League club Chesterfield in August.
The 22-year-old joined the Spireites from Northampton Town for an undisclosed fee in January.
Smith started his career at Barnsley and made 44 appearances for the Tykes, including 25 as they won promotion to the Championship in 2015-16
After leaving Barnsley, he made 38 appearances for Gateshead before signing for Northampton.
He made eight starts and two substitute appearances for the Cobblers.