Is there anything I can use to temporarily hold my dental implant in place? (Photo)

Dental implants are 100% artificial and are not attached to teeth in any form.  You have a root of a tooth still present, and appears hollow as if a post and core were present previously, likely with a crown on top of that.  What remains is not restorable and needs to be extracted.  Then, an implant or a bridge can be placed.

that looks like your own tooth. You might have had a post and crown and now they have come out. You should remove the tooth and have implant. The cost is about 4-5k

You don't have an implant. You appear to have had a root canal done and the post and crown have fallen out. It may be a very simple procedure to recement the post and reuse the same crown if it is not damaged. You can use poligrip to put the post in temporarily but it will not be very secure and may damage the root further. I suggest trying to get into your dentist today for this repair.