Morrison started his career at Manchester United and was tipped as a future star at Old Trafford.
However, after failing to break into United's first team, he joined West Ham in January 2012.
The 21-year-old's time at Upton Park has been beset by off-field troubles, though, and earlier this year he was remanded in custody after being charged with assaulting two women.
On the Cardiff move, Morrison wrote: "Happy to get a three month loan at Cardiff City time to start playing football again."
Cardiff, who were relegated from the Premier League last season, are still on the hunt for a new manager after Ole Gunnar Solskjaer parted company with the club after less than 10 months in charge last Thursday.
The Welsh outfit currently occupy 16th place in the Championship having amassed nine points from their opening eight matches.
