Yes. Banks generally can make changes to a fixed rate, but there are limits to the changes banks can make and certain notice requirements. For credit card accounts, the term fixed rate usually is used to distinguish the rate from a variable rate, which is based on an index.
Banks cannot advertise a rate as fixed unless the ad also says how long the rate will be fixed and that it won't increase during that period.
In general, a bank cannot change your fixed rate for one year after the account was opened. There are exceptions to the general rule. For instance:
If you agreed to an introductory rate that ends after six months or more.
If you are more than 60 days late in making a required payment on your account, the bank can increase the rate that applies to your existing balances and new transactions
After the rate change goes into effect, the bank can apply the new rate to transactions that occur more than 14 days after it sent you the 45-day advance notice. The old rate will apply to transactions that occurred before that.
Review your account agreement for policies specific to your bank and your account.