40 mA absolute maximum rating. Aim for 20 mA.
If Arduino can (safely) source ~20mA per pin, could one use more than one pin to equal required current? Say, if 60mA is needed, could one use three pins to source that to the transistor?
Depending on the package metal or epoxy, the 2n2222a can handle between 500 and 800 mA through emitter-collector and the base is quite happy with 5mA to turn on fully.
It's such a simple circuit.