I don't know of any IRC *programs* that have dice rollers, though there are two pseudo-IRC programs that are free that do:
. openRPG, freeware, open-source and findable on sourceforge.net.
. WebRPG, which is actually dree, despite some of the documentation claiming it's not, but it's no longer supported by, well, anyone. I forget the URL for them, but they should be findable via Google.

As for IRC *servers* who allow/have Dicebots, I only know of one that's any good: RPGWorlds (web: rpgworlds.net, IRC: chat.rpgworlds.net ). You can go into the Help channel and just request a Dice bot, and they'll get one into your channel. The Dice bot is decent, but can't handle any "minus" modifiers to its roll (We were trying to play D&D 3e with it, so you can see the problem there), nor can it handle different *kinds* of dice (We also tried to play Alternity there, so again, you can see the problem, heh).

One note that's not documented about RPGWorlds' Dice bots: If you enter "3d6", it'll just give you a random total of 3d6. It's also possible it'll only give you a random number between 3 and 18, with no weighting (or uneven weighting) towards the bell curve (almost all electronic dice rollers have this problem, though). If you enter "3 d6" (with a space between the first number and the 'd'), it'll give you the three separate rolls.
e.g.:
<Aengus> 3d6
<DiceXX> [Aengus] chanced the fates, and rolled [3d6] to get [14].
<Aengus> 3 d6
<DiceXX> [Aengus] chanced the fates, and rolled [3 d6] to get [4 6 4].

If you're playing WEG Star Wars, this can be useful for determining Force die effects. Just decide at campaign start something like "The last die in the list is the Force die," and always roll with the space in the Dice expression.

Hope this helps!