Wiktionary gives one usage of 鸟 as "(dialectal) to pay attention; to heed; to take notice of"
Which dialect, or what region is this, and how does it look in one or two sample sentences?
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Pls refer to 釋義 No. 10. ==> 〈俗〉 理會，答理
The above meaning matches that in English. It is an expression used in Mandarin.
Ex: 不鸟你。 ==> 不理你
The reason 鸟 is used in conversations(not writings) simply because its pronunciation is derived from 理.
鸟 has some vulgar meaning.
我不鸟你 means I don't care about you.
鸟人 means douchbag
Traditionally, it is a dialectal usage in north of China. It appears many times in the classical book <<水浒传>>, and becomes well known by the whole country.
The truth is 鸟 means 屌.
I think the usage of the word 鸟 originally comes from the word 嬲 which is pronounced the same as 鸟. If you look up the dictionary, you can find that 嬲 means to make fun of（戏弄） and to torment or bother（纠缠）.
In Cantonese, 嬲 is pronounced as nau, which means to be angry with. It's a verb that expresses an emotion. Though this word literally means emotional，but it is usually used to express anger.
我好嬲啊！ =I am so angry!
我嬲你啊。= I am angry with you.
（These are Cantonese, which is used in Hong Kong, Guangdong province, Guangxi province, Hainan province in China, and some other regions and countries all over the world.）
我不鸟你了=我不理你了 These sentences are the same. They all convey a negative emotion which means that I am speechless, I don't want to talk to you anymore, etc, and indirectly means that I am mad at you. I think it's just because 嬲 is more difficult to write and recognize, so people just replace 嬲 with 鸟.
PS: 鸟 is not polite compared to 理 in the sentence 我不鸟/理你了.