Phonetic convergence describes the automatic and unconscious speech adaptation of two interlocutors in a conversation. This paper proposes a Siamese recurrent neural network (RNN) architecture to measure the convergence of the holistic spectral characteristics of speech sounds in an L2-L2 interaction. We extend an alternating reading task (the ART) dataset by adding 20 native Slovak L2 English speakers. We train and test the Siamese RNN model to measure phonetic convergence of L2 English speech from three different native language groups: Italian (9 dyads), French (10 dyads) and Slovak (10 dyads). Our results indicate that the Siamese RNN model effectively captures the dynamics of phonetic convergence and the speaker's imitation ability. Moreover, this text-independent model is scalable and capable of handling L1-induced speaker variability.