Edit: I've found better solution, read about it here.
Let's say you have class:
namespace MyNamespace;
class MyClass
{
    const MY_CONSTANT = 'my_constant';
    const MY_CONSTANT2 = 'const2';
}
Create and register Twig extension:
class MyClassExtension extends \Twig_Extension
{
    public function getName()
    { 
        return 'my_class_extension'; 
    }
    public function getGlobals()
    {
        $class = new \ReflectionClass('MyNamespace\MyClass');
        $constants = $class->getConstants();
        return array(
            'MyClass' => $constants
        );
    }
}
Now you can use constants in Twig like:
{{ MyClass.MY_CONSTANT }}