Augmented Reality (AR) has been applied to education in a variety of subjects, but in comparison to AR in STEM education, research on integrating pedagogical designs with AR in language learning is less mature. This study presents an AR-supported Chinese character learning game designed for young learners and investigates its effects on learners' cognitive engagement in classroom learning. A total of 53 grade 2 students and two teachers from a Singapore government primary school participated in the study. The findings indicate an obvious improvement of students' levels of cognitive engagement in the AR-supported activities. Furthermore, compared with acquiring expert-created content knowledge, students are more continuously engaged in the learning activities designed for enabling self-generated contexts. Suggestions for future system design and pedagogical strategies of leveraging AR to engage young learners in language learning are proposed from this study. The study also provides some insight into how to investigate cognitive outcomes of AR-enabled learning design through analysing learning process.