Yes, you can. (Well, only if you're a child arguing with your siblings about a favoured position in the family car. Otherwise, no. Adults don't talk like this).
Following on from Bramwell and John's replies:
Shotgun ( also 'calling shotgun') is a very American expression. I don't think it's used outside the US.
'Dibs' seems to be universal. It's known in both the US and the UK, and probably elsewhere also. We also have the expression 'First dibs (on something)', if there's an issue of choosing the most favoured option amongst several.
One British expression which may not be known elsewhere is 'Bags' or 'Bags I' or even 'Bagsy'. For example, "Bags I go first on the slide!" or "Mum! It's not fair! Jack always bags the front seat". That's the expression I'm most familiar with. I'm guessing it comes from the idea of shooting or stealing something ( a rabbit or game bird, for example) and claiming it as your own by popping it into your bag.
Anyone know if 'Bags' is also used in Aus/NZ? It's been going for quite a few generations, so it may well have spread to the Antipodes.