Hello Helen;
As far as I know, its not possible to have an annotation shapefile (they are only permitted in GeoDataBases like a '.mdb' or '.gdb').
One workaround is creating a shapefile of polygons that perfectly outline the annotations. The resulting polygons would not be scale dependent. If this is ok, you can use the tool "Feature Outline Masks" and make sure Method/Mask Kind is set to 'EXACT'.
A python script can be made to run this tool, but if you only have to run the tool a few times, I'd suggest not to bother with python.
Let me know how it goes.
Good Luck!