First, she describes why we have not yet answered this question based on good 'ol fossil evidence:
"The reason we don’t know whether T. rex had one is that the organ is generally too soft to leave a fossil trace. (There’s an exception to this: some mammals have a bone in their penis, the os penis or baculum. This can fossilize. Humans are unusual among primates in not having one; in case you’re wondering, it’s not clear whether the bone plays a role in maintaining erections.)"
To summarize the article: yes, she thinks they did. She bases her opinion on a few key evolutionary pieces of evidence. First, the two extant groups most closely related to dinosaurs are the crocodiles and birds.
Male crocs (of Class Reptilia) have a penis they keep tucked inside their cloacae. Unlike mammalian penises, that of the crocodile transports the sperm along an external groove, as opposed to through an internal tube.
The other group related to dinosaurs is the birds (of the violently disputed Class Aves). Birds can be divided into two main groups: those of the palaeognathous and those of the neognathous.
"The palaeos comprises the big flightless birds such as ostriches, emus, rheas, and cassowaries, as well as kiwis and an obscure (but flying) group of south American birds, the tinamous; the neos covers everything else. The palaeos have penises; like crocodiles, they keep them tucked into their cloacae. Again like crocodiles, the organ has an external groove for sperm. What’s more, the lineage leading to the other endowed birds, the ducks, geese, and swans, appears to have split off from that of the other neos relatively early."
All of this informations points to the conclusion that the ancestor of all birds in fact had a penis. At some point early in the evolution of neognathous birds, the penis was lost (and regained in many types of waterfowl in what probably was an independent event. Waterfowl often mate in the safety of the water, and a penis assists in steering the sperm and balance). So crocodiles have one, and ancestral birds probably did, and since the two groups have a very similar genital morphology - it may be safe to infer that T.rex probably had one too!