In general, credit card issuers take about 30 days to review your application. After that, it will be between five and seven business days until the approval letter arrives in the mail. This letter tells you when your credit card will arrive and gives a telephone number to call if you have questions. Give your credit card 10-15 days to arrive after that.
In reality, your credit card may come much faster than that – but allow at least 30 days before pursuing further action.