The short form of currency is commonly curr. It is used as an abbreviation in dictionaries, financial documents, accounting, forms, and general writing.
In international finance, currencies are more commonly identified by their three-letter ISO 4217 codes rather than by “curr.” For example, the US dollar is USD, the euro is EUR, the British pound is GBP, the Indian rupee is INR, the Japanese yen is JPY, the Chinese yuan is CNY, the Australian dollar is AUD, and the Canadian dollar is CAD.
The word currency itself can also be shortened informally to cur., but curr. is generally clearer because it is less likely to be confused with other abbreviations. In a sentence such as “Currency: INR,” however, the word usually does not need to be abbreviated at all.