It is easy to apply for an ICICI credit card. You need to log onto the ICICI Bank website and fill the application form. You can submit it along with the required documents. You can also visit your nearest ICICI branch and submit the application and documentation in person. Typically, it takes up to 21 days for a credit card application to be processed. It is advisable that you make sure you fulfil the eligibility requirements for the particular card you are applying for. This will help avoid probable rejections.