Old English æcer "tilled field, open land," from Proto-Germanic *akraz "field, pasture" (source also of Old Norse akr, Old Saxon akkar, Old Frisian ekker, Middle Dutch acker, Dutch akker, Old High German achar, German acker, Gothic akrs "field"), from PIE root *agro- "field."
"[O]riginally 'open country, untenanted land, forest'; ... then, with advance in the agricultural state, pasture land, tilled land, an enclosed or defined piece of land" [OED]. In English at first without reference to dimension; in late Old English the amount of land a yoke of oxen could plow in a day, afterward defined by statute 13c. and later as a piece 40 poles by 4, or an equivalent shape [OED cites 5 Edw. I, 31 Edw. III, 24 Hen. VIII]. The older sense is retained in God's acre "churchyard." Adopted early in Old French and Medieval Latin, hence the Modern English spelling, which by normal development would be *aker (compare baker from Old English bæcere).