Electric field is a vector. It can point left, right, up, down, forward or backward. In your example it will point from the positively charged plate to the negatively charged plate. Whether you consider that positive or negative depends entirely on your choice of what direction to call "positive" and how you arrange the plates.
If you say that electric fields pointing to the left are positive and ones pointing to the right are negative, and then arrange your capacitor with the positively charged plate on the right and negatively charged plate on the left, then the field will be "positive". But if you turn the capacitor around and put the positively charged plate on the left and negatively charged plate on the right, then the field will be "negative".