Cancun Local: +52 (998) 980 3458
This is a tricky question. Yes and No. Regular taxis are not allowed inside the airport (those from the City), if you want to take one of these taxis, you need to go out of the airport, and by this I mean really outside the Cancun Airport, to the main highway which is about 2 kilometers from the main Cancun Airport building.
The other “taxis” at the airport, are actually private transportation companies allowed by the airport to have a desk there but prices will be really high.
That’s why most people reserve their Cancun Airport Transportation prior to arrival.