Ratchet & Clank on Xbox 360? No — PlayStation Exclusive Since 2002
No Ratchet & Clank game was ever released for Xbox 360. The franchise is owned by Sony (Insomniac Games) and has been PlayStation-exclusive since its 2002 debut.
Ratchet & Clank Timeline (Relevant to Xbox 360 Era)
PS2: Ratchet & Clank (2002), Going Commando (2003), Up Your Arsenal (2004), Deadlocked (2005), Size Matters (2007 PSP/PS2).
PS3: Tools of Destruction (2007), Quest for Booty (2008), A Crack in Time (2009), All 4 One (2011), Full Frontal Assault (2012), Into the Nexus (2013).