Braid spent three weeks on loan at London Scottish in October and has made three competitive appearances for the Warriors.
Glasgow Warriors head coach Gregor Townsend said: "We're pleased that Connor (Braid) will be able to get regular game-time with London Scottish, after impressing there on loan and we wish him all the best in London.
"We're delighted that he will return for a period during the RBS 6 Nations and we'd like to thank London Scottish for their support with this."
Connor Braid added: "I've really enjoyed my three-month spell at Glasgow Warriors and was delighted to sign-off with a win on Sunday against the Dragons.
"I wish everyone at the club all the best for what is a really exciting few weeks ahead and I look forward to returning to help the Warriors for a short time next year."
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