Can you activate Renata Glasc, Mastermind draw ability multiple times?

Yes. Renata Glasc, Mastermind's draw ability — [1][C]: Draw 1 — has no exhaust cost and no "once each turn" limit, so you can activate it as many times as you can pay [1][C] each time.

Two constraints to keep in mind: she must be at a battlefield ("Use my abilities only while I'm at a battlefield"), and each activation has to happen during your Main Phase in an Open State — she has no Action or Reaction keyword, so you can't fire off extra draws mid-Showdown (Rules 145.2, 377.3). Each activation goes on the Chain separately, so your opponent gets a response window between them.

Contrast that with her score ability, which does use [T] (exhaust) — that one is limited by needing her ready, but the draw ability doesn't tap her at all.