In Calcelmo's Laboratory in Markarth, there is a Spider Control Rod that controls a specific dwarven spider called "Aicantar's Spider." Does it work on other dwarven spiders?
It only works on Aicantar's Spider.
Other spiders won't even care.
According to the wiki:
The Spider Control Rod shoots a beam of energy which Aicantar's Spider walks towards. As the spider cannot be interacted with aside from the use of the Spider Control Rod, it does not seem possible for the spider to move outside of the laboratory area. The only other use is during the quest "Hard Answers," using the spider as a way to sneak past the hallway filled with poisonous gas. The rod has no apparent function beyond this.
With the release of Dawnguard, the Dragonborn can attain the Aetherial Staff, which will allow a Dwarven Spider or Dwarven Sphere to be summoned for 60 seconds.