To be able to stand as a constituency or regional candidate at the Scottish Parliament election you must, on the day you are nominated and on polling day, be:
either a British citizen, an Irish citizen, a qualifying Commonwealth citizen, or a qualifying foreign national2
There is no requirement in law for you to be a registered elector in Scotland.
A qualifying Commonwealth citizen is a Commonwealth citizen who either:
does not need leave to enter or remain in the United Kingdom (UK), or
has any form of leave to remain in the UK
A qualifying foreign national is a person who is not a British, Irish, or Commonwealth citizen who has, (or is, by virtue of any enactment, to be treated as having) any form of leave to remain.