This question isn't answerable in the form its asked as the "height of Earth's Atmosphere" is not defined in any meaningful way. The reason for this is that there is no clear ending to the Earth's atmosphere. It tapers off exponentially with height, but it never ends exactly. You could talk about the height of the Karman line changing because the Karman line is defined as the height at which the velocity required to maintain lift is equivalent to orbital velocity. Since the velocity to maintain lift is dependent on atmospheric density the Karman line does change day to day (in its original definition, I am not going to consider the bastardized let's just say its 100Km answer).
Height is not definable, but density at an altitude is. This is the go to metric, so I will answer the question in this form.
Generally aerospace engineers talk about atmospheric density at some altitude as that is a much more usable metric. I posted an example Earth atmospheric model from the MSISE-90 model of the Earth's atmosphere. You can see the density at an altitude of 200km or more often varies by an order magnitude depending on solar activity. This has important effects on satellites and how fast they de-orbit. Satellites will de-orbit faster during high solar activity than low solar activity. This is actually why it is really difficult to predict with high accuracy when satellites will re-enter. Since it is difficult to measure the really low atmospheric densities at LEO altitudes, it is also difficult to predict satellite re-entry times exactly. This is why uncontrolled re-entry dates are given with plus or minus 2 weeks certainty.
Basically density does change, so yes.
Screen shot from http://www.braeunig.us/space/atmos.htm which is archived here
See also Space environment (natural and artificial) — Earth upper atmosphere :