Is it permissible to trade foreign currency by credit card?
Trading different types of currencies is called exchange, or foreign exchange (abbreviated: forex).
While exchanging, the amounts do not necessarily have to be equal but the equivalents must be paid fully at once. To give an example, a sum of US Dollars could be equivalent to exchange 1 British Pound Sterling but it is obligatory to pay the equivalents in advance.
Since both of the exchanged equivalents are currencies, any delay in the payment will be interest and/or ill-gotten gains.
Hence, buying foreign currency by credit card is not permissible.