Lincoln Castle underwent a Â£22m renovation project ready for the document's 800th anniversary.
Castle manager Rachel Thomas said about 34,000 people visited in April - up 21,000 on last year.
Last month, the castle was named as one of 12 sites in the county that could be outsourced to save the council money.
Since the 11th Century castle reopened at the beginning of April, 33,941 people have visited, compared with 12,503 last April.
Lincoln's copy of Magna Carta, is one of only four surviving copies.
Ms Thomas said she had not expected so many visitors.
"Partly, no doubt, the coverage around Magna Carta and the raising in the public consciousness of Magna Carta has helped," she said.
The renovation project included a new wall walk and the reopening of the Victorian prison to visitors.
The high-security underground vault houses the 1215 Magna Carta, alongside an original copy of the Charter of the Forest, which was signed two years later.
The work was funded by Lincolnshire County Council, Heritage Lottery money and private donations.
The authority said a final decision on whether to outsource 12 attractions including the castle, Gainsborough Old Hall and the Museum of Lincolnshire Life has not yet been made.
A castle that had a multi-million pound vault built to house a surviving copy of Magna Carta has almost tripled visitor numbers.