Something that is intact is whole, unbroken, or untouched. Intact is one word, as it has been throughout its history in English. It descends from the Latin intactus (which translates literally to untouched). The two-word phrase in tact doesn’t make much logical sense, as the noun tact has nothing to do with being whole or uninjured. Tact does share a distant Latin root with intact, but the words have always been unrelated in English.
The hyphenated in-tact is also a misspelling.
Mistaken use of in tact in place of intact is rampant, even in edited publications—for example:
While the interior is in tact, the menu is updated and there’s now WiFi, too. [Wall Street Journal]
Core buildings (which house the reactors) have to remain in tact for at least 40 years because dismantling them would release more radioactive material. [BBC News]
He said his players could hit the ice baths with their reputations not only in tact but in many case, enhanced. [Sydney Morning Herald]
The good news is that the correctly spelled intact is more common. Here are a few examples for good measure:
There are few scenarios where I see the structure of our political parties remaining intact after the vote in May. [Globe and Mail]
The 5-4 decision left intact an Arizona tax subsidy that was enacted because the state constitution forbids direct aid to religious schools. [NPR]
Part of my daily route to work took me along a Roman pavement, its original stones intact. [Telegraph]