Scotland Under-21 international McBurnie has yet to make an appearance for the Swans since signing from Bradford City in July 2015.
The 19-year-old featured in three games on loan at Newport earlier this season, and scored a hat-trick on his debut.
Bristol Rovers are currently sixth in the table, nine points outside the automatic promotion places.
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League Two side Bristol Rovers have signed Swansea striker Oliver McBurnie on loan until the end of the season.