You can do that through NFS. Mount the disk to a machine and share that drive through NFS to the other machine.
Suppose the disk to be shared is /dev/sdb and the machines that you want to share the disk is machine1.example.com and machine2.example.com, then:
Mount /dev/sdb in machine1 (You can skip this step if the said disk is already mounted and being used by machine1)
Make the machine1 as the NFS server and export the directory on which /dev/sdb is mounted. Say, if /dev/sdb is mounted on /mnt/sharemount. The NFS export entries in /etc/exports should say:
/mnt/sharemount machine2.example.com(rw,sync)
Now that machine2 is allowed to use /mnt/sharemount from machine1 through NFS from step2, just mount /mnt/sharemount from machine1 on machine2
mount machine1.example.com:/mnt/sharemount /mnt/sharemount
Data will not get corruped if these two machines start writing to the same location in /mnt/sharemount since the required locks will be applied and it will all happen transparent to you.
This answer is only an outline. If you are not familiar mounting a new disk to a server and with setting up NFS, please google how to configure nfs client and server linux. The search results will present you dozens of easy to follow tutorials and step-by-step guides. If you are comfortable using the command line(which I assume you are), you should be able to get the setup done with minimal time.