It all depends
Alright, here's the thing to talk about here.
In general, yes it's art. Simply because of the fact that like all art forms, even down to graffitti, a person can express themselves through it, creating characters, stories, conveying feeling through anime like Piccaso conveyed his through disfigured faces and obcure forms that represented people.
On the other hand, it't become so copy/paste that no one puts any real effort into making anime images. They grab something and make a re-color, call it thier own, and thus is no longer art, it's a stolen work that looks like it's been raped repeatedly and beaten with an ugly stick.
You must also take into consideration that these people in aime and manga are supposed to be people. It's based on lives, characters, real people, therefore are more often than not expected to LOOK like people. That means proper anatomy and proportion, being well versed in the structure of different perspectives and forshortening, scenery and syle.
The main objective of anime is to visually tell a story with moving graphics. A painting alone can tell the tale of the entire universe, but a drawing of a person standing on a blank background tells little more than what that person looks like. There is no dynamic aspect, no story, no life to it. But on the flip side, place that person in a forest, running, speed lines and a bit of forshortening on the forward facing hand, and you've got a story.
Overall, anime IS art, it is just one of the simplest and least defined forms of art there are. Everyone can draw anime (whether it looks good or not), but not everyone can paint like Da Vincci.