Yes, you can set the attributes to fixed height and width.
Select your table and right-click on it.

Choose AutoFit and set it for fixed column width. Then right-click on it again and choose Table Properties. For Rows specify an exact height (the default is an "at least" height).

This will prevent the user from expanding cells by typing. It will not prevent the user from changing them by actually modifying the dimensions.

You can protect the section containing the table and use legacy form text fields or content controls to hold the places for someone to type.

Tables
Making Forms with Microsoft Word