Psychology entrance tests are also available at the universities of Graz, Innsbruck and Salzburg. In many other studies the entrance tests are not required. For many fields of study, the registration deadlines for the restricted studies in the academic year 2020/21 ended on 15 July. However, it is not yet fixed at all universities whether there are actually entrance examinations - some still have deadlines for checking the additionally required letters of motivation, while others still have to complete online self-assessments in the coming days.
Therefore, please enquire in time at the universities of your choice!
An overview of the Austrian university institutions can be found here.