Smith, 28, joined Marine before the 2022/23 season from Cyrmu Premier side Bala, making 45 appearances.
During his time in Wales, the left-back also featured for Wrexham and Connah's Quay and made 200 appearances throughout eight seasons.
He debuted for the Bucks in their 1-0 victory over Avro in the Northern Premier League on Tuesday evening.
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