The problem affects only a small number of handsets sold in the five months after September 2012.
The computer giant said a "very small percentage of iPhone 5 devices" may be experiencing the problem which means owners have to plug them in more frequently than usual to keep up the charge.
They can be replaced free of charge at the company's stores including Buchanan Street, Glasgow, and Braehead near Glasgow.
Once the replacement is fitted, Apple are guaranteeing it for two years after the device's initial retail sale or March 1, 2015, whichever is longer. The battery replacement will not extend your iPhone 5 warranty.
It is the second problem for the handset users. In April, the firm offered to replace the button that sets the sleep/wake mode.Customers can check if their phone will get a free battery by keying in their phone's serial number on the company's website. The recall began in America and China last week. Apple said "If your iPhone 5 is experiencing these symptoms and meets the eligibility requirements noted below, Apple will replace your iPhone 5 battery, free of charge."