Speights recorded seven tackles (three solo) during Thursday's 12-6 win at San Francisco.
Speights recorded 10 tackles (three solo) and a pass defended during Sunday's 21-14 win against the Saints.
Speights recorded eight tackles (six solo), including a tackle for loss, during Sunday's 23-15 loss to the Dolphins.
Speights is expected to start in the place of Troy Reeder (hamstring), who was placed on injured reserve Thursday, Adam Grosbard of The Orange County Register reports.
General manager Les Snead announced Monday that Speights will make the Rams' final roster, Cameron DaSilva of USA Today reports.