You can check your current rank and rank level on the top of the game's main screen, next to your username.

There is a total of 25 unique ranks, as shown below:

  1.  Private
  2.  Private II
  3. Private First Class
  4. Specialist
  5.  Corporal
  6.  Sergeant
  7. Staff Sergeant
  8.  Sergeant First Class
  9.  Master Sergeant
  10. First Sergeant
  11.  Sergeant Major
  12. Command Sergeant Major
  13.  Sergeant Major of the Army
  14.  Warrant Officer
  15.  Chief Warrant Officer II
  16.  Chief Warrant Officer III
  17.  Chief Warrant Officer IV
  18.  Chief Warrant Officer V
  19.  Second Lieutenant
  20.  First Lieutenant
  21.  Captain
  22.  Major
  23.  Lieutenant Colonel
  24.  Colonel
  25.  Brigadier General

How to rank up:

At the end of a battle, the score is added to your total score in your profile. When you reach the required score to level up your rank, you will reach the next level of the current rank. If there is no next level in the current rank, then you will reach the next rank.

This means that if you are currently a Private, you will become a Private II after you level up your rank.

Also, you get prizes when you increase your rank! There are different rewards for each rank, including fuel, cash, and gold! Ranking up also unlocks access to exclusive vehicles, camos, and paints.

The difference between Rank and Level
It is important to remember that ranks are different from your Player levels. Levels are based on the number of battles that you have played, to up the level is only necessary to battle. Ranks are related to your score, which takes into account your performance in collecting 
Experience Points on the battlefield and destroying enemy vehicles.

[Check your Rank]