Avila, 25, faces up to 10 years in prison after pleading guilty to dealing guns without a federal license and conspiracy to deal guns without a license, make false statements in a gun purchase and smuggle goods out of the United States. A sentencing hearing is set for June 25.
Prosecutor Timothy Coughlin told the judge that Avila served as a straw purchaser for the ring and bought 52 guns on its behalf, including two .50-caliber rifles, though the indictment charged him with buying six guns.
There was no mention during the hearing of Terry's death or the guns found at the shootout scene.
Federal authorities have faced harsh criticism since Terry's shooting for allowing suspected straw gun buyers to walk away from gun shops with weapons, rather than arresting the suspects and seizing the guns there.
Terry was killed in a shootout with bandits in a canyon north of Nogales. The shooting broke out as Terry and three other agents tried to catch five suspected illegal immigrants believed to be bandits who rob illegal immigrants as they sneak into the United States.
Manuel Osorio-Arellanes of El Fuerte, Mexico, was shot during the gunfight and is charged with second-degree murder in Terry's death. Osorio-Arellanes isn't charged with being a member of the alleged gun-smuggling ring.
Avila, who hasn't been charged in Terry's death, was accused in the gun-smuggling case of claiming to buy five AK-47 variants and one .50-caliber rifle for himself when he was actually making the purchases on behalf of the ring.
The goal of the U.S. government's gun smuggling investigation was to catch weapons-trafficking kingpins, but firearms agents lost track of many weapons they were trying to trace to smuggling ringleaders, and some guns ended up at crime scenes in Mexico and the United States.
The investigation is the focus of an inquiry by congressional Republicans.
Two other members of the ring also pleaded guilty Thursday.
Joshua David Moore, 23, pleaded guilty to charges of conspiracy and dealing guns without a license and faces up to 10 years in prison.
Kenneth James Thompson, 27, pleaded guilty to conspiracy and faces up to five years in prison.
So far, five members of the alleged gun smuggling ring have pleaded guilty.