Patrick Kiely, of Eleanor Street, Bow, pleaded guilty to the offence committed in February.
The man is already serving six years over the theft of 18 Chinese jade items from Cambridge’s Fitzwilliam Museum.
He will serve 18 months more when that sentence ends, Judge Peter Jacobs at Norwich Crown Court said.
The judge said the rhino head, from the Victorian era, was valued at up to £500,000.
Rebecca Hill, defending, said that Kiely had been forced to take part in the raid and, because it failed, was again forced to take part in the Fitzwilliam burglary.
The attempted theft was made on 20 February when four men entered Norwich Castle Museum and forced open a display case containing the head.
The men grabbed the head and tried to escape, but were disturbed by museum staff who recovered it from them and they were later arrested and charged.
Norwich Castle Museum has since replaced the rhino horn with a replica.
Sold for parts
- Hundreds of rhinos are killed every year for their horns, which are falsely believed to cure a wide variety of ailments, including cancer.
- Between 2008 and 2011, gangs of poachers were said to be responsible for killing more than 800 rhinos, according to monitoring groupTraffic.
- In South Africa, home to the largest wild population, a record 455 had been slaughtered by October 2012. In 2007, 13 were killed.
- The black market value of rhino horns has soared to at least $65,000 (£40,000) per kg in 2012. In 2011, it was about $35,000 (£22,000).
Nihad Mahmod, 19, of no fixed address, was jailed for two-and-a-half years in July for the attempted theft.
On the black market, rhino horns can sell for about £50,000 per kilo.
Kiely also belonged to a gang with three others and a 16-year-old boy who stole Chinese art worth up to £15m from Cambridge University’s Fitzwilliam Museum in April.
All the gang members were jailed over that raid but the art is unlikely to be recovered.
Mr Justice Fulford described that crime as an “act of cultural vandalism”.
He said: “This resulted in the loss to the museum and the public at large, not only in this country but across the world, of pieces of incalculable cultural significance and many millions of pounds in monetary value.
“The likelihood is they passed into private hands and will not be seen again for many generations, if at all.”