Can I catch a wildbird?  

I wouldn't.  Taking a wild bird and putting it into captivity is not fair.  Better to buy a bird that was bred in captivity and has never known any other life.

Not to mention, it is illegal in many places!

Wild Finches belong in the wild.

1. They will not tame.
2. They don't do well in captivity.
3. They can carry diseases
4. It's illegal
5. You can be forced to pay a large fine.

Same could be said about quail,  pheasants etc but there often kept and bread in captivity no?

Im not saying do it is most likely illegal but not so sure its any more unfair then it is to quail and pheasants.

Game birds are a different classification.  Migratory birds and songbirds such as finches are protected, as are most raptors.   And aren't the pheasants and quail that are raised and bred and sold non-native species?  You'd have to check federal and state laws to see which wild birds you can legally possess, and what the permitting process is.

In a single word:

No.

Wild birds do not domesticate well, if at all. I've raised baby sparrows to adulthood and had to keep one because he was not releasable (Pigeons, House Sparrows, and Starlings can be kept without a permit). The baby (who we named Lucky) was never friendly and got worse and worse the older he got. I had him for about three years and he was just an ornery nasty little thing. And this is a bird I raised from a baby.

Birds taken from the wild often have heart attacks and die when put into a domestic situation. Your best bet would be to go to a pet store and buy a zebra finch or one of the other variations. They are very cheap and fairly domesticated.

leghornlover@123 :

I won't I thought it would be easier to catch one

It will definitely be easier to purchase one, both for you and the bird.