ANTAKYA, Turkey—Some Syrian rebel factions have obtained advanced portable antiaircraft weapons, according to rebels and regional officials, a development that could alter the Syrian war's trajectory and fan U.S. concerns that such weapons could end up in the hands of anti-Western Islamist militias.

Video footage uploaded to the Internet earlier this week appears to show rebels in Aleppo using weapons that military experts and rebels say are heat-seeking, shoulder-fired missiles, the first documented instance in the conflict....