Conversational convergence is the tendency for individuals to modify their phonetic speech behaviors to converge with the behaviors of their interlocutors. Evidence of conversational convergence in a native language (L1) is robust, yet research regarding its development in the second language (L2) is sparse. In order to examine the conversational convergence in spoken dialogues, we developed a natural speech corpus in which spontaneous conversations of 15 dyads of English learners were collected and analyzed. The conversational convergence in this paper focuses on the convergence of pitch, which includes the maximum, minimum, and average pitch as well as the pitch range. A personality measure (i.e., autism-spectrum quotient score; AQ) and its correlation with the pitch measures were examined. The results reveal that in this casual board game setting, (a) an English learner tends to use higher f0 max, higher f0 min, higher f0 mean, and a narrower f0 range when speaking in their L2, and most of the pitch values (except f0 max) naturally converge; (b) personality does not directly influence language learners' pitch, but it does influence their speaking rate.