Could someone tell me if a 3.5X10X44mm scope will fit on a Ruger 77(270) with the medium rings, or will it require the high rings? Thanks.

LOW scope rings generally will accept up to a 32mm or smaller scope objective diameter
MEDIUM scope rings generally will accept up to a 42mm or smaller scope objective diameter
HIGH scope rings generally will accept up to a 52mm or smaller scope objective diameter
SINGLE OFFSET scope rings generally will bring scope back 1/2" for eye relief

This is from the Ruger website assuming you have Ruger scope rings. In which case it looks like you need the high rings.

Thanks.