Crocombe, 22, who played just six games in five years for Oxford, left the U's by mutual consent earlier in the week.
He spent time on loan with Barnet and Southport last season, having previously had a spell with Nuneaton.
The New Zealand Under-23 international is yet to earn a senior cap for his country but was included in their Oceania Nations Cup squad in May.
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Carlisle United have signed former Oxford United goalkeeper Max Crocombe on a one-year contract.