Is someone know if is it possible to build a web server on an old Android phone (instead to buy a small Raspberry Pi)? Is it a good idea?

Possible: yes
Good idea: Not really.

@ItsNotMyFault , we have all old unused smartphones in our home. Smartphone have low energy consumption. How it can be a bad idea?

@Madeindjs

Its mostly performance issues, an android phone that will sell for less than a Pi costs is pretty much guaranteed to perform significantly worse.

It depends on what kind of web app you're going to run on that (high CPU load could burn the phone), how old the phone is (is it even powerful enough), and whether you could install a linux distro on it at all (Android OS is not intended to be an OS for a webserver)

@ItsNotMyFault , for example my old HTC One M8 is most expensive than my Raspberry Pi B+. So my HTC should have better specification than Raspberry and may support better an Apache Server, no?