The majority of customers affected by the move, which RBS estimates to be around 200,000, will now be paying a new rate of 4%, up from 3.75% previously.
Customers will have access to a range of alternative products if they feel they wish to switch products as a result of the decision.
RBS says it has had to contend with increased funding costs over the past year and can no longer absorb the cost.
A spokeswoman says: “Over the last year the cost of funds at which we need to borrow at to fund our mortgage commitments has risen considerably. We have absorbed the cost during this period but have now decided to pass on some of this increase, 0.25% to our Offset and TOA customers.”