If you are wondering about causality, then I think that voltage difference $\Delta V$ is fundamental as it is the cause, and the current $I$ is the consequence.
If you want to have current, you need movement of the charges. The most obvious way to move charges is to act upon them with electric field, and each electric field is accopmained with voltage difference.
I real terms I cannot think of the quasi-electrostatic process - and Ohm's law does describe quasi-electrostatic process - in which the current would create the voltage. Hence,
$$I \propto \Delta V.$$
An interesting connection to the interpretation above are constant voltage and constant current sources. Constant current sources are actually voltage sources with quick loopback that changes voltage in order to keep the current constant.