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.
This unsecured card requires no deposit and can help build your credit
Receive opportunities for credit line increases, a fee may apply
See if you Pre-Qualify in less than 60 seconds
Receive 1% cash back on eligible purchases, terms apply
$0-$99 annual fee
$35-$99* annual fee
real credit card for a less than perfect credit
*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.