It is a question of regional usage but according to The Grammarist tire is used mainly in the US and Canada:
Tire and tyre both mean a covering for a wheel, usually made of rubber. Tire is the preferred spelling in the U.S. and Canada. Tyre is preferred in most varieties of English outside North America.
Of course, all English speakers use tire in the sense to grow weary.
This preference appears to be confirmed also by Ngram:
Ngram a tire in BrE vs AmE.
Ngram a tyre in BrE vs AmE.
Advanced systems to monitor fuel and tyre usage give the company a clear picture of how its fleet is performing. [Guardian]
The machinery would enable the factory to produce the latest generation of car tyres, the company said. [BBC News]
He said that he had just returned to Haiti from studying business in Canada, and that he was helping his father run a tire retread factory. [NY Times]
Andretti also worries about drivers who neglect the simple things, such as checking their tire pressures. [Globe and Mail]