Data publishing is a practice consisting in preparing certain data or data set(s) for public use thus to make them available to everyone to use as they wish. This practice is an integral part of the open science movement. There is a large and multidisciplinary consensus on the benefits resulting from this practice. The main goal is to elevate data to be first class research outputs.There are a number of initiatives underway as well as points of consensus and issues still in contention. 
To publish your research data, you will need to identify an appropriate repository for your content. You can discuss your options with your Subject Librarian who will be aware of data publishing repositories.
You can also search for a repository to publish.
re3data is a data repository registry. re3data provides searching for research data repositories from different academic disciplines. It presents repositories for the permanent storage and access of data sets to researchers, funding bodies, publishers and scholarly institutions.