<p>People affiliate with others who share their psychological traits. Does the same phenomenon occur with AI instructed to mimic human psychology? Large language models (LLM) were prompted to use language that mimicked anxious symptoms or their absence (Experiment 1; n = 100), extroversion or introversion (Experiment 2; n = 100), and an exact mirror or inverse of participants’ personality (preregistered Experiment 3; n = 100). With full knowledge that they were interacting with an artificial system, participants engaged in written interactions with both LLM versions and then evaluated their engagement. Those with anxiety reported a stronger connection to the LLM that mimicked anxiety, a distinction also reflected in the sentiment of the messages they exchanged. Extroverted participants affiliated more with the AI that mimicked extroversion. Finally, when participants interacted with LLMs that mimicked either their own personality profile or the inverse of their personality (i.e., the opposite pattern of their Big-Five scores), they reported more affiliation with the LLM mimicking their personality; this distinction was also reflected in the sentiment of their messages. Results support affiliation in human-AI interactions based on the linguistic presentation of a shared psychology. We propose that through <i>socioaffective</i> tuning, LLMs might achieve greater human-like correspondence.</p>