No, you can't have the field expand the way you want. You can achieve what you want when you print the record - you can have the print slide up (and across) to remove dead space. So you could have data entry into a field with a scroll bar, and then print from a dedicated print layout.
If the amount of data is small, but it's just that the filed is even smaller, a useful compromise sometimes is to have the field's tooltip display all the data when you mouse-over.
I know they are not exactly what you asked for; they are compromises that sometimes ease the problem in particular circumstances.