How can I fix a cracked floor tile in my kitchen without replacing it

Your question is like asking how to fix a burned out lightbulb without replacement. Broken is broken and it needs to be replaced. You should ignore it until you are ready because anything you paint or pour on will give an unsatisfactory result. You could use a throw rug.

In case there is someone who has a solution to offer you should specify whether your tile is ceramic, vinyl, porcelain, stone or wood. They are different.

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IF you have a matching tile or can get one, you can fix this. Tape the border around the cracked tile (outside of the tile behind the grout line). You will have to break out the cracked tile. use a chisel, flat head screw driver, to help you break it and remove it completely down to whatever it was glued down with. Remove all the tile and glue, and clean up the grout into a smooth edge so that the new tile will fit in place. "Butter" the back of the new tile and put it in place. Get some grout that matches the color of the rest of floor, and grout around your new tile. You just need to follow the direction on the grout to put it down. Shouldn't take you more than a hour.

How to Repair Holes or Cracks in Ceramic Tile

Patching unwanted holes in glazed tile like this can be a tricky proposition. Here's a solution that may not always be perfect, but will make a big improvement. Polyester resin or auto body filler, often used to repair car bodies. Mix up a small batch by adding some hardener and stirring it thoroughly. Using a putty knife, press the resin into the hole slightly overfilling it. Then just as the material begins to harden while it's somewhat rubbery, trim off the excess with a razor blade.

Next use 600 grit sandpaper to sand the filler smooth. Wetting the paper with water makes it work best. Now it's time to try and match the color of the tile. A porcelain touch up kit which is available at most home improvement centers comes with several different colors of paint. You can also use artists acrylic paints available from Michaels, Hobby Lobby, art supply stores, and online.

The trick here is to mix these different colors together until we come up with one that matches the tile. Apply the paint with a small brush. You can test it on a nearby tile. When you get it the way you want it, then just paint over the patch and let that dry. Give it one final sanding with that very fine sandpaper and you'll have, well, maybe not a perfect match, but something that's a heck of a lot better than what you started with.

Simple to fill crack with grout, carefully wipe off any excess. When dry, use acrylic craft paint to match grout color to tile color. Paint this on grout with tiny, pointed artist brush. Then, seal with a couple of coats of clear nail polish.