Yes. When you create a slashtag using the create slashtag form, choose the option on the bottom of the form to “Make this slashtag private. Only I can see and use it.” This will create a private slashtag that only you can see and use. You will need to be logged in to use this slashtag.
Once a slashtag is private, it cannot be made public. If you wish to make the slashtag public in the future, you will need to delete it and re-create it as a public slashtag.