Updated answer:
In current OS X and iOS, Dispatch objects are now treated as Obj-C objects by ARC. They will be memory-managed the same way that Obj-C objects will, and you should use strong for your property.
This is controlled by the OS_OBJECT_USE_OBJC macro, defined in <os/object.h>. It’s set to 1 by default when your deployment target is OS X 10.8 or higher, or iOS 6.0 or higher. If you’re deploying to an older OS, then this is left at 0 and you should see my original answer below.
Original answer:
Dispatch objects (including queues) are not Obj-C objects, so the only possible choice is assign. The compiler will throw an error if you try to use strong or weak. ARC has no impact on GCD.