The robots, known as Spheres (Synchronised Position Hold, Engage, Reorient, Experimental satellites), currently have limited capabilities.
It is hoped the smartphones, powered by Google's Project Tango, will equip the robots with more functionality.
The robots have been described by experts as "incredibly clever".
When Nasa's robots first arrived at the International Space Station in 2006, they were only capable of precise movements using small jets of CO2, which propelled the devices forwards at around an inch per second.
"We wanted to add communication, a camera, increase the processing capability, accelerometers and other sensors," Spheres project manager Chris Provencher told Reuters.
Founded in 1997 with the ambitious goal to develop a robotic humanoid soccer-playing robot by 2050, the RoboCup is an annual robotics competition that sees robots play soccer against each other in an exercise of AI and applied robotics.
Each year of the competition also features a robot-on-human soccer game. And every once in a while, the robots will score a goal on the humans, just as they did this year in the above GIF.
They've happened in the past, but robot-on-human soccer goals at RoboCup are becoming a bigger deal. It's simply a function of goal quality being so dramatically improved over years before — robot AI is increasingly capable of masterminding some soccer strategy on our flesh-and-blood would-be Beckhams, and then putting that strategy to work effectively.