As others have said, having seen
Doctor Who is certainly not a prerequisite for watching
Torchwood.. That being said, as
Guy Gardener said, season 2 of nu
Who set up
Torchwood and the two-part finale introduced it, however it introduced a very different
Torchwood than you see on the show (which is explained on both shows).
The main character, Captain Jack Harkness, was introduced in season 1 of nu
Who and spent several episodes travelling with the Doctor. The end of
Torchwood's first season dovetails with the end of
Doctor Who season 3, though you can find the clips on YouTube, but they aren't necessary, if you're fine with a character disappearing and not knowing where they went.
A first season episode features a classic-
Who villain, which most
Who fans hated
Torchwood's take on. It's directly linked to the season 2 finale of
Doctor Who. A late season 2 episode fills you in on the characters and how they came together to work at Torchwood, which has a few nods to
Who, but nothing blatant.
In short, having seen
Doctor Who will fill in details, but it is not necessary. It compliments
Torchwood and may increase your enjoyment, in terms of understanding things, but
Torchwood is not that complex, that missing that knowledge will hurt your understanding or enjoyment of the show.