Yes, astrology is a science...
And even more: "It is at once an art, a science and a wisdom" wrote the philosopher Raymond Abellio. It was taught as such in the main French and European universities until the middle of the 17th century. We were then talking about astrology "natural" astrology.
In France, the last official astrologer was Jean-Baptiste Morin, known as de Villefranche. He was physician to King Louis XIII and professor of mathematics at the Collège Royal (today's Collège de France). He was a very much listened to adviser to Cardinal Richelieu. When he ceded his power to Mazarin, the latter said to his successor: "I bequeath Morin to you."
When Galileo discovered that it is the earth that revolves around the sun and not the other way around, we moved from a geocentric to a heliocentric conception of our universe. Astrology was then quickly abandoned because its foundations no longer corresponded to the new astronomical reality. However, the famous astronomer Kepler pointed out that for any terrestrial observer, the sun and the other stars continued to make their revolutions around the zodiac and that the new discovery did not change anything...
In other words, astronomy is the science of the sky as it is, and astrology is the science of the sky as men see it. And just because these views are different doesn't mean one is true and the other false.
Astrology is a science because it includes a part of observation – it is therefore an exact science – and a part of interpretation that is based on rules confirmed by two thousand years of experience – it is therefore an experimental science. Finally, it is a conjectural science when it formulates forecasts: only in this case is it susceptible to error because a forecast is based on a convergence of factors showing a more or less marked trend. The more factors there are and the greater their convergence, the more likely it is that the predicted event will occur.
However, no one is surprised that the same procedure is used in medicine: the patient's observation is based on the patient's observation to formulate a diagnosis and possibly a prognosis (pronoscere : know in advance).