In most cases, you can cancel the credit card with no additional fees or charges after receiving your bonus points so long as you have paid off your balance in full. However, you may be charged the annual fee or a percentage of that fee based on how long the account has been active. If your credit card has $0 annual fee for the first year and you cancel within the first 12 months, you may be able to avoid this. Check with your provider to find out if fees will apply.