To the highest precision, it is
currently tilted 23.439 degrees measured from the perpendicular to the Ecliptic.
Earth's axial tilt varies from 22.1° to 24.5° over a 42,000 year period. The tilt is currently decreasing. In addition to this variation there are nutations of about 0.005° caused by differences in the plane of the lunar orbit.
The axis itself does rotate, but much less, much shower. It takes 26000 years to finish one cycle. The Stella Polaris (North Star, Polar Star, or Ursa Minoris Alfa) hasn't always been the northernmost star.
It's important to understand that the Earth is not actually tilted on its axis. The axis of the Earth is tilted relative to something else. The initial plane of reference is the Ecliptic which is the imaginary disk enclosed in the circle the Earth traces around the Sun every year.
For some reason long lost in antiquity, the "normal " disposition of the Earth's axis is seen as right angles to the ecliptic. Yes, VERTICAL. The axis of the Earth is tilted 23.5 degrees from that vertical, with the North Pole permanently directed at the Polar Star. That is, 66.5 degrees from the ecliptic.
Sometimes you may hear that earth's 'inclination' is about 7.25 degrees, but this refers to the inclination of earth's orbital plane in relation to the sun's equator. This is different from the tilt of earth's axis in relation to earth's own orbital plane.
Compared to the plane of the Milky Way galaxy, the Earth is tipped at about a 60 degree angle. The Sun orbits the center of the Milky Way in about 220 million years, carrying all of its planets along with it.
We cannot yet figure out which way the Milky Way galaxy is moving, although since everything else is moving, it would be strange indeed if the Milky Way was standing still!