"Moderate, well-organised fighters from the Hazm movement have for the first time received more than 20 TOW anti-tank missiles from a Western source," the source said on condition of anonymity, and without specifying who had supplied the rockets.
The Hazm movement, part of the opposition Free Syrian Army, brings together mainly ex-army officers and soldiers who defected from the military to join the revolt.
"More have been promised should it be proven that the missiles are being used in an effective way," the source said.
Amateur video distributed by the opposition Masarat media network showed rebels unpacking, loading and firing several missiles at unnamed locations in the Syrian countryside.
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"Most of the targets were tanks," said the rebel official, adding that "the 20 missiles have been used 100 percent effectively, always hitting their targets."
Vastly outgunned by the army, rebels have frequently called on the West to provide them with specialised weaponry.
Syria's uprising was initially peaceful but later escalated into a brutal insurgency after the regime launched a massive crackdown on dissent.
More than 150,000 people have been killed, and nearly half the population has been displaced since the revolt began in March 2011.
Western supporters of the revolt have hesitated to arm the rebels for fear that weapons may fall into the hands of powerful jihadist groups.
Government loyalists backed by Lebanon's Shiite Hezbollah movement have meanwhile made a string of advances near Damascus and in central Syria.