While you can give a hint to the runtime engine via System.gc() this is a "hint" and not a command so you cannot rely on it to actually trigger garbage collection. Even if it were a command, forcing garbage collection is unlikely to accomplish what you want- the garbage collection process itself consumes resources so when it runs your game will be impacted. So, in fact, you want to avoid garbage collection to ensure your game isn't contending with the GC process for resources, see this link for a libgdx specific discussion: http://code.google.com/p/libgdx-users/wiki/ForceGarbageCollection
Instead of dynamically allocating many short lived objects that require garbage collection I think the better strategy would be to allocate long life objects at times the user isn't playing, e.g. loading screen or first start up. These objects can even be returned to a pool when no longer needed and then reused as necessary.