Theoretically speaking the ideal way of getting reduced rate of interest is to have a good credit report. It goes to your advantage and gives you power to negotiate with the company, prompting them to issue cards carrying lower rates of interest. Other than that, a low interest credit card is offered to a chosen category of people from working class like military personnel and people having certain disabilities.
Then, there are credit card companies offering special discounts to frequent fliers, and to people holding low interest business credit cards. On using your credit card for buying essentials like food and clothing, you are charged a very low, almost negligible APR.