Q:

Do I use a plural or singular verb after "half"?

When we describe a pie chart that gives information about percentage of common reasons for travel to a country, which of these two is correct?

As it is mentioned above, half of visitors has a trip for vacation
As it is mentioned above, half of visitors have a trip for vacation

A:

I would reword the whole thing and use the past tense because the pie chart reports statistics that were accurate when they were recorded. 

As  mentioned previously, half of the visitors stated that the trip was for pleasure.

Notice that the term trip is in the singular, so the auxiliary  is singular too.
As trips are often categorized as being for pleasure or business, I chose to say pleasure   instead of  "vacation".  In fact, the expressions business trip and pleasure trip are idiomatic in English.
If the statistic hovers around 50%,  e.g., 48.9%, 51.2% then use an adverb such as: approximately, nearly, almost, close to or just under/over  half

Approximately 50 percent of all visitors stated that their trip to (NAME OF COUNTRY) was for a vacation.

Examples found on Google Books

Approximately half the visitors (53%) had season tickets and just under half (47%) were male 

Festival and Events Management

Notice that the plural verb agrees with the subject visitors
N.B the preposition "of" can be dropped from half of, as seen in this example taken from the Bentley University research survey.

Ranking second  as a pre-trip influence and representing over half    the visitors (53%) reported they also used printed brochures,
  maps and travel guides to help plan a visit.

