There are two choices - soldering iron soldering and torch soldering.
I'd recommend torch soldering as the end result blends with the metal better
PLUS if you need to, you can still hallmark it.

You can join them using soft solder using a soldering iron but it isn't as durable
(because the metal of the jump rings can't get hot enough to melt and mix with the metal in the solder).
You would ideally use a torch to apply enough heat to get a good solid join.

For jump rings, it's probably easier to use paste solder, since it stays exactly where you put it.
Paste solder is a mixture of solder, flux, and a carrier (makes the mixture flow and stay where you put it).
You can buy paste solder in a syringe, which makes it easy to apply with precision.

Paste solders are sold with names such as hard, medium, easy, and extra easy.
They indicate the temperature at which the solder melts (not how easy they are to use ).
Hard solder melts at a high temperature and extra easy solder melts at a low temperature.
If the name of the solder is followed by a number, then that is the temperature at which the solder melts.
Personally, I would recommend medium solder for jump rings ~ but easy works too.

Hard, medium & easy are all suitable for pieces to be hallmarked (not sure about extra easy, don't think it is).

1) Close all of the jump rings to be soldered so that their edges are flush with each other.
Solder can't bridge gaps, but it will flow down the joint between jump ring edges (capillary action).

2) Apply the paste solder to your joint. Apply the solder to the inside of the ring,
so it contacts the joint on both sides of the ring.
The amount of solder you use should be about the thickness of the wire.

3) Hold the link you are working on over the edge of the solder block
(to help protect the rest of the chain from heat) and heat.
Apply the flame so that both the right and left sides of the joint are heated evenly until the solder flows,
focus the heat on the ring not the solder. You should be able to watch the solder flow through the joint
and come out on the front of the ring. When the solder flows remove the heat immediately.

4) After all of the jump rings have been soldered then pickle the cooled jump rings to
remove any oxidation or flux residue. If you want you can neutralise the pickle by rinsing
the jump rings in a water with a bit of baking soda (sodium bicarbonate).

This movie might help if you want to pre-solder some of the rings (easier off the chain) http://www.youtube.com/watch?v=nYVl35kvKHs

Nic x

P.S> These are guidelines not instructions and are followed at your own risk, don't burn yourself or
set fire to your hair yadda yadda yadda