Credit Cards
No one disputes the illegitimacy of ribaa (usary - interest) in Islam. The Qu'ran clearly points out this forbidden transaction (2:275-276; 2:278-280; 3:130; 4:161; 30:39). Similarly, any transactions that contain ribaa whether in part or in whole are also haram (prohibited).
A business transaction in Islam is regarded as halal or haram based on not only the final outcome of the transaction, but also based on the actual contract that is entrusted. Within the contracts which govern credit cards, there exists the implicit usage of ribaa or interest which the user agrees to if they fall short of paying the "loan" in the specified time period. This is where the use of credit cards become haram.
The Holy Qu'ran has prohibited riba in general terms which includes all the forms of riba whether or not prevalent at the time of its revelation. When the Holy Qu'ran prohibits a transaction, it is not a particular form of the transaction that is meant by the prohibition. It is the basic concept of the transaction which is hit by the injunction.
When liquor was prohibited it was not only the particular forms of liquor available in those days which were forbidden, it was the substance of liquor which was banned, and nobody can reasonably claim that the new forms of liquor which were not available in the days of the Prophet (SAW) are not hit by the prohibition. When Qimar (gambling) was declared as haram the purpose was not to restrict the prohibition only to those forms of gambling which were in vouge at that time. The prohibition, in fact, encompassed all its present and future forms, and no one can sensibly argue that the modern forms of gambling are not covered by the prohibition.
Similarly, ribaa has many concealed forms in the modern world and infiltrate into our daily lives. It is our responsibility to discover whether modern business transactions are halal or haram.
Fourth paragraph taken from The Historic Judgment on Interest by Muhammad Taqi Usmani
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Selected Fatawa on Credit Cards
Staying Away from Doubtful Actions
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Forbidden Business Transactions