The young Scot signed for Villa in January 2022 from Dundee United.
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Smith had a short loan spell with St Johnstone in 2024.
He was called up into the Scotland U21 squad for the first time in October last season.
Speaking about signing for Barrow, Smith said: “I’m absolutely delighted to get going, get on the training pitch, start playing games, and I just think it’s a good move for me in terms of where I’m at in my career.”