Some studies indicate that the solar modulation of galactic cosmic ray (GCR) particles has profound consequences for Earth's climate system. A corollary of the GCR-climate theory involves a link between Earth's magnetic field and climate, since the geomagnetic field also modulates the GCR flux reaching Earth's atmosphere. In this study, we explore this potential geomagnetic-climate link by comparing a new reconstruction of the Holocene geomagnetic dipole moment with high-resolution speleothem data from China and Oman. The speleothem δ18O data represent proxy records for past precipitation in low-latitude regions, which is a climate parameter that is likely to have been sensitive to variations in the GCR flux modulated by the dipole moment. Intriguingly, we observe a relatively good correlation between the high-resolution speleothem δ18O records and the dipole moment, suggesting that Earth's magnetic field to some degree influenced low-latitude precipitation in the past. In addition to supporting the notion that variations in the geomagnetic field may have influenced Earth's climate in the past, our study also provides some degree of support for the controversial link between GCR particles, cloud formation, and climate.