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Gaius Gracchus's reforms in 123BC saw the introduction of the practice of Tax Farming were the burden of tax collection was reassigned by the Roman State to private individuals or groups known as Publicani.
In essence, these individuals or groups paid the taxes for a certain area and for a certain period of time and then attempted to cover their outlay by collecting money or saleable goods from the people within that area
(source)
It has been suggested that the Publicani used a primitive system of credits and debits to transfer tax revenues back to the Aerarium. Several ancient writers have recorded this practice and referred to it as Permutatio. Cicero for example, used a Permutatio while governing Cilicia to send funds to Athens.
It is not clear, how widespread this practice was. Other systems of credit transfer or cash-less transfers such as Nomina, Syngraphae may have been used to send revenues back to Rome. (source)
Such systems reduced drastically the requirement for the physical transfer of cash which could have been expensive and dangerous in itself. In such cases, cash was transferred in the form of bullion or in actual coin.
It is also possible that tax money from a particular province was generated by selling goods aquired through tax farming. In such cases, the Publicani would ship their saleable goods to Italy where the profits of sale would be then physically transferred to Rome.