Can a student from overseas make a credit card in Singapore?

Yes, as long as you hit the requirements set by the banks.

But your choices are limited to be honest.

If you are not 21 years and above, you can forget about it.

Otherwise, most banks require the foreigner to be working and earning a relatively high annual income before they grant the foreigner the credit card. This is to safeguard their interests, since there is a risk, no matter how small, that the foreigner can incur huge debts and just leave the country.

Some banks will accept fixed deposit of a certain amount as an alternative to the income requirement but they are in the minority.

There is a card that accept students though. Go google CITI Clear Card and that might help.