Texas resident Araceli King received 153 computer-controlled “robocalls”, which continued after she had asked the company to stop.
US district judge Alvin Hellerstein said Time Warner Cable had acted in a “particularly egregious” manner.
The company said it would review the ruling before deciding how to proceed.
Making unwanted automated calls is illegal in the US, and companies breaking the rules can face a fine of $1,500 for each call.
Mr Hellerstein said he had tripled the penalty for Time Warner because it had made 74 calls to Ms King after she had registered her complaint.
The judge said any company that “robodials the same person hundreds of times over many months without pausing to wonder why it cannot reach him” could not complain about the higher fine.
Crackdown
The US made it illegal to make unwanted automated calls in 2009.
Since then the Federal Trade Commission has announced a “crackdown” on the practice.
The law says marketers must have written permission from a person before robocalls can be made, although exceptions are made for surveys or if the subject matter is political or to do with a charity.
In June, online payment service PayPal updated its user policy to suggest that its US customers would have to agree to accept automated marketing calls and messages before backtracking over the issue.
The Federal Communications Commission (FCC) enforcement bureau chief Travis LeBlanc has said “customers are not required to consent to unwanted robocalls or robotexts”.
UK complaints
On 2 July, the UK’s Information Commissioner’s Office (ICO) said it had received a record number of complaints about nuisance calls in the past year.
It received 180,188 complaints, of which 45% were about automated calls that played a recording down the telephone.
Consumer watchdog Which is running a campaign to make company executives accountable for the nuisance calls their firms make.
“Regulators, government and industry must work harder to cut off unwanted calls and texts that annoy millions of us every day,” said the organisation’s executive director Richard Lloyd.
