WASHINGTON—Having carved out a leading position in the software that runs cellphones, Google Inc. is now angling for a role in the networks that connect them.

That isn’t to say the Internet giant wants to set up thousands of cell towers to compete with carriers like AT&T Inc. and Verizon Communications Inc. Instead, it is lobbying U.S. regulators to free up vast amounts of low-cost, mostly vacant spectrum that could serve as an alternative to the big carriers’ services.

...