I have looked at different Singaporean credit card offers, Visa and MasterCard, and I couldn’t find an exception. It may be a law in Singapore that a credit card applicant needs to be 21 to apply for a credit card.

Requirements for RBS credit cards
• You must be between 21 & 65 years of age.
• Singapore Citizens & Permanent Residents: Minimum income is S$30,000 p.a.
• Foreigners: Minimum income is $60,000 p.a.

Requirements for HSBC credit cards
Applicants must have a minimum income of S$50,000 p.a. and be at least 21 years of age.

http://www.creditfast.com/scripts/prodView.asp?idproduct=271

Most credit cards offered by banks in Singapore require you to have a minimum of $30,000 income. But I do know there are some banks that doesn’t require that amount, one of them is Citibank:

http://www.citibank.com.sg/SGGCB/APPS/portal/loadPage.do?tabId=Credit%20Cards&path=/prod/det/cc_xx_clr_card.htm

I’m pretty sure there are other banks that offer something similar. Usually if you can’t find it written on the website itself, you have to download the application form for respective cards. You can then read the terms & conditions in the form.

If not, why not consider a debit card instead? You don’t need to have a minimum income for it, and there’s no forgetting to pay bills