"The horns of dehorned rhinos have been observed to grow back rapidly and without deformity, reaching slightly less than full size after three years" - Gulland, Williams and Beddington 1994 "Is Dehorning African Rhinos Worthwhile?" Pachyderm no. 18
However the backstory to this photo notes that the poachers may have actually sawed into the skull of this animal which could complicate or compromise horn regrowth.
Incidentally this is the first time I have heard of poachers sawing off a horn but leaving the individual animal alive. It seems unusual that poachers would have access to and knowledge of the appropriate tranquilizer dosage for a full grown White Rhino, and also pretty risky. Anyone know more?
A very unusual and controversial conservation action was taken in Namibia [Lindeque 1990] and Zimbawbe [Kock 1989] by removing the horns of both black and white rhinos [Ceratotherium simum] so that the poachers would be less likely to kill them. In order to determine the efficacy of the "dehorning" method, a study [1] was conducted to determine:
rate of horn regrowth and the subsequent monetary worth of the horns
whether the vulnerability of dehorned rhinos or their neonates is altered with respect to poachers and predators.
During the study, data was gathered in Namibia in 1991, 1992 and 1993; and based on this data, the study makes some conclusions. The ones important for this question are:
horn regrowth is rapid, averaging nearly 9 cm of total horn per animal per year, a finding that suggests new horns on an average animal were worth $1775-7750 one year after dehorning.
since poachers fail to discriminate between large- and small-horned rhinos, recently-dehorned rhinos may not be immune from poaching. However, neither horned nor hornless rhinos differed in their vulnerability to poachers more than four years after the initial dehorning.
The front horn of a white rhino averages around 90 cm [2] [reaching as much as 150 cm]. So, from all the data, one can say that the complete regrowth of the horn may take up to 10 years, although it's much more likely that the rhino will be dehorned or poached before that.