It ran down her leg, causing the most serious burns near her hoof.
Placer County Animal Services are investigating the incident, which occurred in Penryn, a community about 60 kilometres from Sacremento.
The Humane Society of the Sierra Foothills has offered a $US3000 reward for information leading to the arrest and conviction of the offender.
Betsy's owner, Bob McClurg, told Horsetalk it was the second time that Betsy, who came into his family through the Bureau of Land Management's burro adoption programme, had been attacked with acid.
The first time was about five years ago.
Bob said he was away at the time of the most recent attack, around the middle of last month.
Because it had happened before, his wife Shannon immediately knew what had caused the burns.
"Betsy was running in the irrigation line," he said. "She was either trying to wash it off, or found the water soothing."
Shannon called the vet, who put Betsy on antibiotics and ordered the twice-daily application of a soothing ointment.
Betsy has been with the McClurgs since she was around a year old.
She was only a baby when captured in a bureau wild-horse muster.
Betsy and her mum ended up at a petting zoo at Disneyland, but the young burro had a tendency to nip.
"She was returned back to the the BLM and we got her," Bob explained.
The daily attention has seen the wounds heal up well.
The family surmises that the acid was either poured or sprayed on, perhaps even with the water-cannon type of toys some kids have.
Betsy has a campanion on the McClurg's five-acre roadside property - a male burro called Jesse James.