Looking on the internet deeply has found these results:

authorize is the most popular phrase on the web.

authorise 19,500,000 results on the web	authorize 165,900,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Without an invitation from the police, I cannot authorize an investigation. The president requires daily proof of life to authorize the release. Because the director wouldn't authorize Them joining the investigation. I can authorize a lot of things for you. Tell him Parliament must authorize a greater British presence here in the colonies. I cannot authorize any action at might result in the President's death. Tell the tower to authorize takeoff. In order to authorize the UCITS, some information on the management company is needed.

authorise

19,500,000 results on the web

authorize

165,900,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Without an invitation from the police, I cannot authorize an investigation.
The president requires daily proof of life to authorize the release.
Because the director wouldn't authorize Them joining the investigation.
I can authorize a lot of things for you.
Tell him Parliament must authorize a greater British presence here in the colonies.
I cannot authorize any action at might result in the President's death.
Tell the tower to authorize takeoff.
In order to authorize the UCITS, some information on the management company is needed.