Firstly you have to be 21 years old or above.
Secondly the requirment for applicaiton of credit card is usually local/PR need s$30,000 per anuum income and foreigners s$60,000 per annum for Classical MasterCard/Visa, and s$45,000(local) s$60,000 for American Express/ Gold Mastercard/Visa.
Ether support by Income Tax of Assessment of CPF statement. Some accept computer-generated payment slips also
If you have enough income can apply.
Heard some banks will issue credit card to those who deposit certain amount in there bank, but never found one... :P