There are many types of pensions that can be accepted by credit cards. Compare credit cards here.

Regardless of your income source, you will normally be required to prove that you have an annual income of at least $15,000.
It mostly depends on your income. If your pension is your sole source of income, your choices will definitely be more limited than they would be if you had income from employment, a business or investments, since some banks do not accept pensions as a valid type of income for some of their cards.
The other limiting factor may be the amount of your pension. Even the most basic credit cards will often have a $15,000 minimum income requirement, while prestige cards offering rewards points and other complimentary benefits may have a much higher annual income requirement.
A pensioner may be simply be looking for a low-cost option to provide a more convenient payment method than carrying cash, with the added benefit of a line of credit able to be accessed in an emergency. In this situation, the ideal card would have a low (or zero) annual fee, and preferably a low interest rate on purchases in case a short-term financial emergency arises. It would also be a good idea to compare the amount of any other fees, including late payment fees, over limit fees, foreign currency transaction fees and lost card replacement fees.
However, pensioners may also be self-funded retirees enjoying an affluent lifestyle involving travel, eating out and regular shopping trips. Their choice of card will be dictated by their circumstances and spending pattern, and they would probably be better served by a more expensive card offering rewards points and other complimentary benefits, such as travel insurance.
You will need any of the following documents that apply to your situation:
It may help if you have had a relationship with a particular bank for many years. The application process may be simpler because the bank has access to your financial history. However, your current bank may not be offering a card for which you qualify, or which is most suitable for your circumstances. You are not limited to applying for a credit card from your current bank.
The lowest credit limit available for most cards is $500, regardless of whether you are a pensioner or a wage earner. The card issuer will determine the level of credit they consider suitable for your financial circumstances, but you can choose to have a lower limit than the one they recommend.
Definitely not. Apply for only one card at a time, and avoid making multiple applications within a short time period because this could damage your credit score. If your first application is rejected, contact the card issuer’s customer service department to find out if there is any further information you can provide to make them reconsider their decision. Do this before deciding to apply elsewhere, because you may be rejected again if you have not provided sufficient proof of your creditworthiness.