Construction of human-curated annotated datasets for abstractive text summarization (ATS) is very time-consuming and expensive because creating each instance requires a human annotator to read a long document and compose a shorter summary that would preserve the key information relayed by the original document. Active Learning (AL) is a technique developed to reduce the amount of annotation required to achieve a certain level of machine learning model performance. In information extraction and text classification, AL can reduce the amount of labor up to multiple times. Despite its potential for aiding expensive annotation, as far as we know, there were no effective AL query strategies for ATS. This stems from the fact that many AL strategies rely on uncertainty estimation, while as we show in our work, uncertain instances are usually noisy, and selecting them can degrade the model performance compared to passive annotation. We address this problem by proposing the first effective query strategy for AL in ATS based on diversity principles. We show that given a certain annotation budget, using our strategy in AL annotation helps to improve the model performance in terms of ROUGE and consistency scores. Additionally, we analyze the effect of self-learning and show that it can additionally increase the performance of the model.