Having a list of alien plant species naturalised in an area and knowing their invasive potential (i.e. a post-border species risk assessment framework) and the precise locations where they are found, are now a priority as a management strategy to curb their spread, avoiding damage to ecosystems and saving management costs. This is especially important in arid ecosystems, which are particularly vulnerable to impacts due to their limited resources. Weed Risk Assessment systems (WRAs) analyse plant traits that influence their invasive potential through a set of questions whose answers score taxa according to their invasive potential. In this work, we identify potentially invasive plants inhabiting the arid southeast of the Iberian Peninsula, the driest region in Europe, by compiling alien plant species recorded in the wild and applying the Australian and New Zealand Weed Risk Assessment (AWRA) system. The AWRA applies scores that evaluate species characteristics related to biography, undesirable attributes and biology/ecology for establishment elsewhere. We provide the dataset obtained in the application of the AWRA test: a list of the alien plant species naturalised in the study area and their geographical distribution; the answers, scores and results of the test, as well as the scientific sources that support the existence of such characteristics in these species. We found that 64.4% of the 177 taxa assessed can be considered potential invaders. This database represents a useful and transparent tool for environmental managers to deal with the problem of plant invasions effectively. It can also be confronted with data from other areas of the world where these species are naturalised.