How can I set the PHP version in PHPStorm?

In case your field is disabled.

Probably your settings "Synchronize IDE settings with composer.json" is enabled

You may change your PHP version in composer.json file

"require": {
    "php": ">=7.1.0",
}

OR disable your settings in this path

File -> Settings -> Languages & Frameworks > PHP > Composer

*If you change your composer.json file - As Félix Gagnon-Grenier commented, Keep in mind it has effects on the way packages will be required later

So, you mean to highlight all pieces of code that will not work with the PHP version you are writing it in, right? That can be done here:

Preferences -> Languages & Frameworks > PHP

and the same on Mac:

PhpStorm -> Preferences (⌘,) -> Languages & Frameworks > PHP

Or with newer versions of PhpStorm in Windows:

File -> Settings -> Languages & Frameworks > PHP

then select your PHP version, for example, 7.0

This is very useful when your local system runs PHP 7.0, for example, but production is running PHP 5.5.

That way PhpStorm will warn you which parts will not work in production, show proper hints during writing code according to the selected version, etc.

You can use Alejandro Moreno's answer, but sometimes you might not be able to change PHP level from closed dropdown.

You can disable "Synchronize IDE settings with composer.json" checkbox from:

File -> Setting -> Languages & Frameworks -> PHP -> Composer

And after applying again open

File -> Settings -> Languages & Frameworks -> PHP

Here You can change PHP level from opened dropdown.