Yes, store credit cards are generally available even for bad credit. Sometimes you have even better options with unsecured regular credit cards.
Lets assume, your credit score is in hight 500's, then your best bet will be Capital One QuicksilverOne or Capital One Platinum cards
If your score is in mid 500's you can apply for Credit One Bank® Platinum Visa® for Building Credit, or a Milestone Gold credit card.
Applying is quick and easy with our fast decision process
Less than perfect credit is okay
24/7 access to your account information, even on mobile
Card designs to fit your personality at no extra charge
Account history is reported to the three major credit bureaus in the U.S.
$35-$99* annual fee
*Dependent on credit worthiness
Among store cards JC Penney's is the one that can probably approve you with a score in low 500's.