Could anyone explain why do we use rat IgG as a control rather than PBS injections in mice.

this has only resulted in me thinking of sugar mice mmm

Unfortunately I am reminded of the great plague.....

to determine nonspecific binding of rat
monoclonal antibodies to mouse cell surface antigens e.g. in FACS etc.. ....?

What an odd question.. were you asked this at interview or something?! :P Hehe!

Sounds to me like a method of showing non-specific binding or agglutination, as someone else has said....