This open source project does re-ordering using jQuery and the JavaScript Client Object Model - you should be able to adapt it for your needs.
http://sprello.codeplex.com/
The bulk of the code needed to do this is in WebPart.js -
http://sprello.codeplex.com/SourceControl/changeset/view/178c1d245922#SPrelloAssets%2fWebPart.js
Specifically
// If we have an order field to use then work out both what this item's order ID should be
// and update all other items in that column at same time
if (this.OrderField != null) {
var cards = card.parent().children();
for (i = 0; i < cards.length; i++) {
var itemId = $(cards[i]).data("listId");
if (itemId == mainItemId) {
mainItemOrder = i + 1;
}
else {
var item = this.List.getItemById(itemId);
item.set_item(this.OrderField.get_internalName(), i + 1);
item.update();
}
}
}
The rest of the code is for configuring it for different lists - something you may not need so you could do this as just a javascript file with no web part to deploy.
As Alexander mentioned - you're going to have performance problems with large lists, something to think about.