You must be an Australian citizen, permanent resident or a New Zealand citizen to apply for the ACT Government graduate program.
If you are a visa holder at the moment and you are looking to gain permanent residency you can absolutely apply you would just need to have permanent residency before the end of the calendar year you apply in.
This is the same for your degree, which must be completed before the end of the calendar year.
Do you have a question for ACT Government or any other graduate employer? Ask it here!