How many calories should a 44 year old woman weighing 163 lbs and 4'4 in height take per day?

It depends how much you weigh and your activity level.

You can start by calculating your BMR (Basal Metabolic Rate).

Women: BMR = 655 + ( 4.35 x weight in pounds ) + ( 4.7 x height in inches ) - ( 4.7 x age in years