Is there any way of bonding teeth without drilling them?

Like anything it depends. Generally its recommended to very lightly roughen the tooth surface.  This enables the filling material to stick better.

Dear mor909, It all depends on the purpose
of the bonding and the aesthetic result you want to achieve. If there's decay or
an old restoration, the bonding can’t be done properly without removing those.
If it's done to add the missing tooth structure or to enhance the smile,
drilling might not be necessary.

It is possible to perform bonding without drilling but there are a few things that are affected:1.  Beveling the tooth prior to bonding helps to blend the filling shade into the tooth and minimize or eliminate the appearance that the filling is there. 2.  Beveling the tooth creates more surface area to bond, the more surface area to adhere to the stronger the bond strength. 3.  Beveling the tooth creates more surface roughness which will will create a stronger bond the a more smooth (uncut) surface. 

Yes, it is possible to add to the tooth structure to improve aesthetic tooth appearance without drilling the tooth so ask your doctor about the different options you can get.