Parents often wonder what size violin their child needs. Whether you are buying or renting your instrument, a reputable music store will be able to help you out.
Basically, your child should hold the instrument under their collar bone and against their neck and with their left arm outstretched. The scroll of the instrument should hit the middle of the palm of the hand and the fingers should be able to wrap around the scroll. This will ensure that the instrument is the proper size.
For more detailed information, I would recommend the following link, which gives recommendations in inches, although the best way to size a violin is to have your child with you. The link is: http://www.childrensmusicworkshop.com/instruments/violin/violinsizingguide.html