My sister just turned 16 and she suffered from anorexia nervosa, but now when she got her period will she be able to grow taller?

Likely some growth: She is only sixteen and likely her growth has been suppressed/not optimal by poor nutritional intake. If she is well now and able to consume adequate calories for growth, she likely will grow some. The amount of grow she can catch-up depends on how severe her anorexia was/is and genetic influence (how big/tall parents are) etc..Make sure that she followup with doc regularly. I wish her well.

Growing taller: Unfortunately - while an can stunt growth - her final height will depend on whether her growth plates in her long bones have closed. Generally by age 16 the plates have closed and your final height is set. Her menses will definately be influenced by an since the hormones needed - estrogen and Progesterone are made from food.

Possibly 1-2 1/2inch: The elaboration of hormones capable of supporting menses signal the final stages of linear growth in females. You can usually expect between 2 and 2 1/2 inches after the first cycle, regardless of how irregular they are for the first year.