Can invisalign fill my missing teeth gaps? (Photos)

Orthodontically moving the teeth may be only part of the solution to close your spaces.  I would recommend seeing a cosmetic dentist to have a comprehensive cosmetic workup to determine what the best treatment would be.  I would think that a combination of a limited orthodontic treatment followed by some sort of restorative procedure on your lower front teeth will give you the result you are looking for.

There are several options for replacing missing teeth.  Sometimes the situation is such that orthodontics can close all of the space but from your photo, you may not fall into that category.  Therefore, moving the teeth to create a good space for a replacement tooth may be part of the solution but ultimately  a good restorative dentist will need to  discuss the best tooth replacement options with you.  No matter what option you choose, having the right amount of space so that a natural looking "replacement" tooth (either implant, bridge or cantilevered pontic) can be added will probably be part of the plan.  Creating this ideal space is where the orthodontist comes in.
You may want to start with a prosthodontist, a dentist who specializes in more complex tooth replacement cases, and see what he or she says about your options and they may have an orthodontist who they have worked with in similar cases.   Don't give up just because you are not an ideal implant case.  There are lots of other options available.