First Financial was hit with the penalty by the Information Commissioner's Office (ICO) following an inquiry by the watchdog.
The fine comes after 4031 complaints were made against messages sent from numbers that the ICO found to belong to First Financial.
The messages included some claiming to be from the recipient's friends, reading: "Hi Mate hows u? I'm still out in town, just got £850 in my account from these guys www.firstpaydayloanuk.co.uk."
The spam texts were sent using unregistered sim cards, a common method used to avoid detection.
However, the content of the message was similar on each occasion and referred recipients to a website belonging to firstpaydayloanuk.co.uk, a trading name used by First Financial.
The Privacy and Electronic Communications Regulations, which govern electronic marketing, require organisations to have an individual's consent before sending marketing messages by text.
The Advertising Standards Authority also took action upholding complaints made by members of the public who had received unsolicited text messages.
In October, First Financial's former sole director, Hamed Shabani, was prosecuted at City of London Magistrates' Court after he failed to notify First Financial's processing of personal information with the ICO.
This is a legal requirement under the Data Protection Act. Mr Shabani was fined £150 and ordered to pay £1180.66 costs, despite trying to claim he had no affiliation with the company.
Anyone who receives an unsolicited text message should avoid replying and report the message using the survey on the ICO website.
More than 200,000 responses have been sent in since the survey was launched early last year.