Works for me on a clean install;
screen-3.9.4-2, ircii-4.4-7, glibc-2.1.2-7.

Do you have anything odd in your ircii configuration?

It seems to work if I set my TERM to e.g. vt102, but if TERM=xterm,
there will be a core dump.

Works OK here, in the console, xterm, & gnome-terminal.

What does `rpm  -V termcap` say - do you have a modified
termcap?

--- rpm -V termcap ---
S.5...GT c /etc/termcap
---
--- rpm -q termcap ---
termcap-9.12.6-15
---
--- ls -la /etc/termcap ---
-rw-r--r--   1 root     adm        548317 Jan 28  1999 /etc/termcap
---

Originally, this was a Redhat 5.2 box but I upgraded it to Rawhide.
That might have left something behind.  I haven't edited the termcap
file, and it didn't help after re-installing termcap RPM either -- rpm
-Uvh didn't seem to replace the old termcap.

I did 'rpm -e --nodeps termcap' and installed it again.  Now rpm -V
reports nothing and the file looks like this:
--- ls -la /etc/termcap ---
-rw-r--r--   1 root     root       434898 Mar 29 19:08 /etc/termcap
---

However, it still dumps the core.

Here's a part of strace if it's of any help..
------- strace irc --
ioctl(0, TIOCGWINSZ, {ws_row=28, ws_col=112, ws_xpixel=0,
ws_ypixel=0}) = 0
open("/dev/tty", O_RDWR)                = 3
ioctl(3, TCGETS, {B38400 opost isig icanon echo ...}) = 0
ioctl(3, SNDCTL_TMR_STOP, {B38400 opost isig -icanon -echo ...}) = 0
--- SIGSEGV (Segmentation fault) ---
+++ killed by SIGSEGV +++
-------------------

Aha. You're running the rawhide libtermcap, correct?

It's horribly horribly broken. Don't use it - it might even open
up security holes.
Downgrade to the 6.0 errata version, or wait for libtermcap-2.0.8-17,
which will be in next Raw Hide release.

Libtermcap was indeed causing this.

Thanks for the diagnosis!