Is this for a high frequency situation? RF? The cable size looks like RG174. You can get BNC Male connectors to fit RG174 in several styles. But you will need to be prepared to terminate the connection properly if this is for a high frequency/RF application.
And does the other end of this cable also terminate in a male BNC? If so, you can just buy a new BNC male to BNC male cable and replace the whole cable to avoid needing to mess with installing the connector. If you haven't installed coaxial connectors, there is something of a learning curve to get the strip lengths, etc., correct.
Amazon carries both sorts of things. Just search for RG174 BNC.