Yes. New members are automatically assigned an ID. You can set the base number for those IDs using the setting "Base Number" in Member Settings.
If for instance you set a base number of 5000 - the next new member would receive a Membership ID number of 5001. If someone already has that number, the system goest to 5002, etc.
Note that the system will start numbering at the highest number that is taken. It won't necessarily try to "fill in gaps" between existing members. So if someone has 5001 and someone has 5005 - the next new member gets 5006. We've found that this creates more consistency in member numbering (so two members added near the same time don't have wildly different numbers).
URL path to the setting: yourdomain.com/settings/module/memberships/#id_membernumberbasenumber