The word "farm" appeared in the late 14th Century. It meant a fixed payment or rent.
But the word is not of Anglo-Saxon origin, it is from Old French, "ferme", meaning to rent or lease; which, in turn, was from Medieval Latin, "firma", meaning a fixed payment.
By the 15th Century, the word had come to connote an area of leased land, but the modern usage of "cultivated land" wasn't used until the early 16th Century.
And, the word "farmer" was first used in English in a very different sense--it meant one who collects taxes or debts.