Giricek had two points in seven minutes in his Suns debut, a 97-92 win over the Blazers.
Giricek, waived by the Philadelphia 76ers on Friday, joins his fifth NBA team. The 6-foot-6 Croatian played parts of six seasons with Memphis, Orlando and Utah before being traded to Philadelphia last Dec. 29.
Suns general manager Steve Kerr called the 30-year-old Giricek "an excellent shooter, a solid defender and a proven playoff performer."
He shot a career-best 42.6 percent from 3-point range for the Jazz in 2006-07. He has averaged 9.6 points in 362 NBA games.
The Suns also signed forward Linton Johnson to a second 10-day contract.