On a former phone I had this as my startup tile for Google (nice):
Incidentally, this appears to be an alternative (also nice):
But I'm stuck with this:
which is nothing other than the default pin-to-start cropped version available for any website and which is less elegant than the other two.
I know Google popped up with a custom "pin to start" option when I first loaded it on the new phone but I think I goofed it up. And since then I've never managed to get that option to reappear.
The accepted solution no longer seems to work - the "pin to start" option doesn't appear even after deleting history.