Correct spelling, explanation: the noun warrant originates from Old North French warant and from Frankish warand. The verb warrant comes from Old North French warantir. As you can see, in each of these forms we have two -a vowels, not -a and -e. It has remained so until today, that’s why the only correct version is warrant, not warrent.

Definition of warrant:
1. noun, a reason for doing something
There is no warrant for such behavior.
I don’t think you need the warrant to go wherever you like.
2. verb, justify or necessitate
I warrant his actions because he was brought up poorly.
The movie I saw wasn’t good, but it doesn’t warrant the insulting criticism.

Collocations with warrant:
Some most commonly used collocations include: a warrant for someone’s arrest, a warrant to inspect, and enough to warrant further.

Incorrect spelling, explanation: there is nothing in the etymology to indicate that this spelling is correct. Before writing down a word, we have to look at its origins. The right form should include two same vowels -a. Therefore, you can be sure that the only correct version of this word is warrant, not warrent.