What you have there is called a "Barrel" connector. Since you have provided nothing to allow us to see the scale, there are three things you'll need to measure:
Inside Diameter (ID)
A simple way of doing this is to grab your set of drill bits, and carefully insert them, smallest to largest, until the size you chose doesn't fit. This then means that the size of the inside is somewhere between the one that fit and the one that doesn't. For example, if my 5/64" (1.98mm) bit fits, but my 3/32" (2.38mm) is too big, then I'd guess I've got a 2.1mm ID. Be sure to use the dull end of the bits.
Outside Diameter (OD)
The most common size is 5.5mm (~7/32"), or about the diameter of a NATO 5.56mm round, if you happen to have any lying around. This is easy to check if you have calipers, but if you don't, then just use a Crescent (R) wrench, adjust the jaws to fit the outside of the barrel, then measure the span of the jaws.
I happen to have a simple drill bit index guide that has all these holes. I just line up the right one(s), and read the numbers. Most any hardware store should have them.
Barrel Length (L)
Most people forget this one. Just measure the usable length of the barrel from tip to where the insulation starts. This is important, as some jacks are deeper than others, and too short a barrel either won't make contact, or wind up falling out due to lack of friction/torsion. A minor quibble is whether it's a straight lead or right angle type. I prefer straight leads, as they don't tend to rip out the guts of your project if you forget to unplug it before moving (provided the plug is in the back - if it's on either side, it really doesn't matter much).
You didn't set your location, but if you're in the Yew Ess uv 'merica, Jameco has a very comprehensive section where they will match up the adaptor to whatever plug you need (if it's non-standard). Although, since you mentioned that it's a 12VAC@3A, I'd go out on a limb and say you're got a 2.5mmID- 5.5mmOD- 10mmL. Now, if you meant "AC to DC adaptor" in your post, it still wouldn't matter too much, as the rule-of-thumb for barrel plugs is to use the 2.1mmID for anything up to about 1.5A. Use 2.5mm for anything more.
If you just need a good one-off adaptor, Radio Shack should still stock their "Adapt-a-plug" series. You should find an "octopus" mess of cables nearby to match the plug/socket (they use letter designations), then buy the adaptor and matching plug (if it's not already included). I've got a few of those tips, too.
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