Generally speaking, yes, your card issuer can raise your interest rate. However, it cannot do so in the first 12 months after you open the account and it can’t do it without giving you 45 days’ notice, unless:
If you close the account before the rate hike takes effect, the issuer may increase your monthly payment so that you pay the balance off in five years. Or it may double the percentage of your balance used to calculate your minimum payment, which will also result in a faster repayment.