What is the ruling of the Sharia on not repaying debts incurred through a credit card and ignoring calls from the bank?

It is permissible to issue and use a credit card as long as it does not include usurious conditions, such as an increase in the amount upon late payment, because every loan that draws a benefit is usury.

The debt resulting from using the card for purchase or cash withdrawal is a fixed debt that must be paid when possible. Procrastination by one who is able to pay is injustice, whereas the insolvent person must be given respite, as Allah Almighty says: "And if there is any difficulty, then wait until a time of ease."