Look for stained glass suppliers - there is a technique called 'copper foil' where you wrap the edges of a piece of glass (or china) with adhesive copper foil strips (like thin sellotape) and then solder the pieces together by applying solder to the foil. I'm sure there are tutorial vids out there to show you what I mean! You could wrap each piece and then solder jump rings to either end, to join them in the way you say - the kit you need isn't too expensive - about £15 for a soldering iron, £4 for foil, less for solder and flux. It's quite addictive, and you could use the same tools for glasswork too! I wonder if, as an alternative, you could use an epoxy adhesive to glue them to silver or metal bracelet blanks - they do exist but I can't think where I've seen them, sorry. But they have loops or holes at either end.
You could also use plaster or mortar to cover plant pots outside (or indoors!), or within a rockery if you've mortared together the rocks (I've always wanted to do this - blue and white china looks stunning with green leaves). Or make a table-top. Or a wall mosaic (floor wouldn't stand up to use). Or a mosaic top for a wooden box. Google Kaffe Fassett and mosaics and see how he uses broken china to great effect. Or buy the book! I can really recommend it - very inspirational and fab photos and instructions.
I am an avid collector of broken china, particularly blue and white bits out of peoples' gardens and fields. 
I've done it all my life and now have literally crates of the stuff. I've made some pieces into mirror frames and pendants using the copper foil technique - but would warn you that they're not the strongest way to link many pieces - the more you have, the heavier the frame will be and it will eventually fall apart. 
A small mirror frame should be ok though.
Some jewellers use high-fired china shards (porcelain, etc) to make pendants, and they use a different technique - make a bezel out of sterling silver to fit the piece and then gently press the bezel in onto the shard. You need it to be high-fired (i.e. hard) because you often use heat in this process and don't want the china to break. Finally (phew, you say), I know that some people who work with precious metal clay (PMC) which fires in a kiln/with a torch to fine silver, use porcelain shards - it's trickier, I think.
(
at how I've gone on. I'll admit it - I'm a broken china geek!)