The 27-year-old former University of Arizona player was waived by the Indiana Pacers on Saturday. He is in his seventh NBA season and has also played for Houston and Minnesota.
Budinger averaged 4.4 points in 49 games with the Pacers this season. He has averaged 8.1 points and 3.1 rebounds for his career.
The Rockets drafted Budinger in the second round in 2009. He averaged a career-best 9.8 points with Houston in 2010-11.
The Suns also signed forward-center Alan Williams to a 10-day contract. Williams, undrafted out of UC-Santa Barbara last year, played in China this season.