Try applying online for a secured card, it's meant for low spenders with either little credit history or a default on loans:
https://www.capitalone.com/credit-cards/secured-mastercard/
The difference between a secured card and a regular (unsecured) card is that you have to make a deposit, which serves as collateral when you don't pay.
You get everything you can expect with a starter card:
>low starting credit line (~$200)
>shitty APR (25%)
>basic benefits: 24/7 customer service, auto rental and travel insurance
If you're approved (which shouldn't be a problem unless you're bankrupt), then put the deposit in, charge moderate amounts to the card, and make payments on time. In a few months, you should be able to apply for unsecured cards with higher limits and lower interests.