I'm assuming you're looking for ranks below the officer grades in the army under the Empire?

A soldier would start as a recruit (tiro) for a period of 4 months at which point he took the oath and became a full soldier (miles).

As a miles there were several grades that determined things like pay and fatigues:

• munifex: had to do fatigues, regular salary
• immunes: no fatigues, regular salary
• principalis sesquiplicarius: no fatigues, 1.5x salary
• principalis duplicarius: no fatigues, 2x salary
• principalis triplicarius: no fatigues, 3x salary

Then you had honours or tasks, a beneficarius was an assistant to a tribune or prefect, curator was one tasked with a specific mission/duty, a magister directed the artillery, discentes were instructors.

Above the common soldiers were the centurion who was in charge of the century (80 men). He had an adjutant/second in command, the optio. There was also the standard-bearer (signifer) and the commander of the guard (tesserarius).

Sources: Goldsworthy: The Complete Roman Army, Le Bohec: The Imperial Roman Army

Edit: fixed century for cohort.