Hampshire-based Onecom was the subject of 1,050 complaints, the Information Commissioner's Office (ICO) said.
The firm, based in Whiteley, is run by Aaron Brown. He was recently acquitted of the manslaughter of his friend who died in a powerboat crash in 2015.
ICO said Onecom could not provide evidence to explain the source of the data used to send the 1,050 messages.
It said the firm was also unable to prove it had consent to send the messages.
ICO said Onecom confirmed it had sent 3.3 million text messages between 1 October 2015 and 31 March 2016.
Steve Eckersley, ICO head of enforcement, said: "Spam texts are a real nuisance to millions of people across the country and this firm's failure to follow the rules drove over 1,000 people to complain."
Anyone bothered by a spam text is urged to report it, either via the ICO's website or by forwarding the text to 7726.
In March, Onecom chief executive Mr Brown was cleared of the manslaughter by gross negligence of Ryan McKinlay who died when a jet-powered boat, driven by Mr Brown, crashed into a cruiser off the Isle of Wight.
A telecoms firm has been fined Â£100,000 for sending millions of spam texts about mobile phone upgrades.