Sharing data and code are important components of reproducible research. Data sharing in research is widely discussed in the literature; however, there are no well-established evidence-based incentives that reward data sharing, nor randomized studies that demonstrate the effectiveness of data sharing policies at increasing data sharing. A simple incentive, such as an Open Data Badge, might provide the change needed to increase data sharing in health and medical research. This study was a parallel group randomized controlled trial (protocol registration: doi:10.17605/OSF.IO/PXWZQ) with two groups, control and intervention, with 80 research articles published in BMJ Open per group, with a total of 160 research articles. The intervention group received an email offer for an Open Data Badge if they shared their data along with their final publication and the control group received an email with no offer of a badge if they shared their data with their final publication. The primary outcome was the data sharing rate. Badges did not noticeably motivate researchers who published in BMJ Open to share their data; the odds of awarding badges were nearly equal in the intervention and control groups (odds ratio = 0.9, 95% CI [0.1, 9.0]). Data sharing rates were low in both groups, with just two datasets shared in each of the intervention and control groups. The global movement towards open science has made significant gains with the development of numerous data sharing policies and tools. What remains to be established is an effective incentive that motivates researchers to take up such tools to share their data.