You can not apply for a credit card by yourself until you are at least 18 years of age. This does not mean that you will automatically be approved for such a card when you become an adult. 

Legally you are allowed to apply for your own credit card at 18, but the law on the subject mandates that you possess a steady income source in order to qualify. Your parents’ monthly allowance will not be counted as income. Only with a reliable monthly income will you be able to repay charges that you make on your credit card so that you do not fall into a credit card debt trap.

When you are ready to apply for a first card, you should be on the lookout for those credit cards that target students. You might also apply for a retail credit card. Both types have a higher chance of approving you when you are just getting started as financially independent. 

Another good choice is to obtain a secured credit card. By making a deposit, you gain a credit limit against this security. Two of these that are great for first time credit card holders are:

  1. Capital One Secured Master Card
  2. Discover It Secured

Both are tailored for you when you start to build up credit on your own.