The continuous-rod warhead in a Sidewinder will rip the hell out of an aircraft, which is made of tinfoil wrapped around complications. A rock from space, by contrast, is made out of rock wrapped around rock.

Assuming charitably that the missile could generate an intercept, you would probably get some sparks, maybe more or less depending on how much of the rock is actually nickel and iron. But basically, the rock is a rock. An AIR-2 Genie likely wouldn't bother it all that much beyond maybe a surface glazing and some neutron activation. The most a Sidewinder will do is expensively nothing.