Siege frigates have light armor. Therefore, the best ships to use to take them out would be either fighters, or (if your enemy has a dangerous amount of flak as well) heavy cruisers.
Another option would be to build a starbase on one of your worlds - in addition to being able to quickly destroy large numbers of enemy frigates, you can also get an upgrade which prevents loss of planet ownership due to bombardment. The AI should keep bombing your world anyway though - with your starbase making quick work of the enemy fleet, your other ships can take out the siege frigates.
Also, is your game updated to the most current version? (1.33 Trinity/Diplomacy) I heard that siege frigate spam was a more common tactic before, but in my (few) recent games against AI I've rarely seen them build more than two siege frigates at a time. A somewhat recent patch changed AI build behavior so that they would only build a few siege frigates at once.
Starbases are strong against Disciples, but so are long range frigates: the LRM, the Assailant, or the Illuminator. So in addition to building a starbase you could build a fleet of mainly LRF. LRF are also relatively good against enemy capital ships.
Edit: Oh, you're playing Vanilla, lol. Well OK, then if the enemy has mainly siege frigates, light frigates, and capital ships, then your best bet would be to build heavy cruisers and long range frigates.
A strategically cheap but effective strategy is to build a few turrets, which do incredible amounts of damage to light frigates and capital ships. If you do that and can lure the enemy fleet into their range, the enemy fleet will very quickly go down.