You get a feat at every odd level, so that is 7 at level 13 regardless of class. As a ranger, you get Endurance as a bonus feat at 3rd level and additional combat style feats at 2nd, 6th, and 10th levels, for a total of 11. However, your archetype takes away the combat style feat at 6th level, so you drop back down to 10, or 11 if your character is human.
Number of feats:
Are you Human? +1
Are you Half-Elf? +1 (skill focus feat,)
Level 13 character: +7 (gained at 1,3,5,7,9,11,13)
Combat style feats: +2 (gained at 2, 10 - beastmaster gives up the 6th level feat)
This would be 9 (or 10 if you are human or half-elf).
This doesn't count the weapons and armor feats they get for free as a warrior class: Weapons(simple,martial), Armor (light, medium, shield).