Not really. That would have been the Ferguson rifle, experimented with by the British, but more or less abandoned when Ferguson was wounded at Brandywine.
Rate of fire six to ten shots per minute, versus one or less for the Kentucky long rifle.
The Americans, however, were the only guys to field actual effective units of riflemen. It should be noted, however, that these were "special forces" units, and the vast majority of American troops, Continental and militia, used muskets just like the Brits.
To go along with that, the colonists also introduced (or at least honed) a gorilla warfare tactic (compared to the previously honorable line-up-and-shoot-each-other game of chicken they called war. In one book I read many years ago, it is thought that this tactic was born of organized chaos. As small groups of fighters would hit and run, or set up ambushes before armies were formed (Battle of Concord) Allegedly, these tactics were adopted and used as the military became more organized. This is where the "special forces" allegedly started.
According to history, when the Brits were confronted at Concord by gathering militia (Paul Revere) the famous confrontation was won by the Brits as Colonists retreated. It was what followed that eventually had them running for their lives back to Boston. The Brits were decimated along an 18 mile retreat that baffled the Kings soldiers. It is thought that most of these colonists were still on their way to Concord and the battle along the British retreat drew them in to set up and take shots. The sniper (rifleman) was born as the colonists fought from positions with cover.
“While at Concord we saw vast numbers assembling in many parts; at one of the bridges they marched down, with a very considerable body, on the light infantry posted there. On their coming pretty near, one of our men fired on them, which they returned; on which an action ensued, and some few were killed and wounded. In this affair, it appears that after the bridge was quitted, they scalped and otherwise ill-treated one or two of the men who were either killed or severely wounded, being seen by a party that marched by soon after…On our leaving Concord to return to Boston, they began to fire on us from behind the walls, ditches, trees, etc., which, as we marched, increased to a very great degree, and continued without the intermission of five minutes altogether, for, I believe, upwards of eighteen miles; so that I can’t think but it must have been a preconcerted scheme in them, to attack the King’s troops the first favourable opportunity that offered, otherwise, I think they could not, in so short a time as from our marching out, have raised such a numerous body, and for so great a space of ground. Notwithstanding the enemy’s numbers, they did not make one gallant effort during so long an action, though our men were so very much fatigued, but kept under cover.” - Colonel Francis Smith (British account of the engagement)