Hi Vadim. Are you using an Aesop theme or another WordPress theme? All Aesop themes have the Aesop Social icons integrated but other WordPress themes most likely will not.
Aesop Social is moreso about properly sharing your content on the web with the integration of Twitter meta data, Facebook og data, Google+ verification, etc. The social icons displaying is a perk of using the plugin within an Aesop theme.
With that said, if you’re using a third party WordPress theme that doesn’t support Aesop Social, you are welcome to utilize the icons via the PHP hook
Full documentation on Aesop Social is available at https://aesopstoryengine.com/product-documentation/ (including information about the hooks/filters). If you’d like to learn more about using Aesop hooks/filters, please read over our blog post on the subject at https://aesopstoryengine.com/tutorials/using-aesop-filters/