Eric Raymond, The New Hacker's Dictionary, third edition (1996) goes on at great length (two full pages) about the differences between kluge and kludge, the fact that kluge is the older and (for most definitions given) preferable term, and the different supposed etymologies of the two words (kluge "from the German 'klug', clever; poss. related to Polish 'klucza', a trick or hook" and kludge "appears to have been derived from the Scots 'kludge' or kludgie' for a common toilet, via British military slang" but "apparently became confused with U.S. kluge during or after World War II"). I have my doubts about this rather elaborate explanation.
It seems far more likely to me that people heard the word kluge spoken before they saw it spelled, and in trying to reproduce the word in writing, some of them chose the spelling kludge. If that is indeed what happened, the spelling owes nothing to the Scottish words kludge and kludgie—which, by the way, are not so much a part of traditional Scots English as to have earned a place in Chambers Scots Dictionary (1911). The entries in Chambers jump from klot ("to scrape up mud, dung, ashes &c.") to klyock ("the last sheaf in harvest") with nary a kludge to be seen.
In contrast to The New Hacker's Dictionary, third edition, Oxford Dictionary of Computing, sixth edition (2008) has a notably succinct entry for the term (which it spells kludge):
kludge Informal An inelegant but effective mechanism (software and/or hardware).
Merriam-Webster's Eleventh Collegiate Dictionary (2003) does not hazard a guess as to the term's origin, but treats it as a word in in good standing:
kludge or kluge {origin unknown} (1962) : a system and esp. a computer system made up of of poorly matched components — kludgy also kludgey adj.
That definition seems out of date as a description of what most people mean by the word kludge today. The American Heritage Dictionary of the English Language (2011) does a much better job:
kludge or kluge n. Slang 1. A system, especially a computer system that is constituted of poorly matched elements or of elements originally intended for other applications. 2. A clumsy or inelegant solution to a problem.{Probably alteration of mid-20th century American military slang kluge, complex device with a simple function, perhaps of imitative origin or perhaps after the Kluge (paper feeder), a piece of printing equipment first manufactured in 1919 by Brandtjen & Kluge, Inc., and reputedly difficult to repair.}
George Mills, Platen Press Operation (1953) offers a possible explanation of why "Kluge" might have become associated with mixing and matching parts from different manufacturers:
The Kluge automatic press consists of a platen press similar to the hand fed machine described in chapter III, with the Kluge feeder attached. The feeder was designed to be attached to presses of other makes and was produced for ten years before the company began making presses. It may still be purchased without the press.
So it's possible that pressmen at companies that added a Kluge paper feeder to a different-make press might have come to speak informally of the hybrid machine—or the add-on part—as "a kluge."
In any event, to return to the poster's question, the latest American Heritage Dictionary confirms that using kludge to mean "A clumsy or inelegant solution to a problem"—the meaning that the poster seems to have in mind—is common in recent U.S. English usage. According to AHDES, the term kludge itself is "slang," and similarly, Oxford Dictionary of Computing calls the term "informal." But the Eleventh Collegiate doesn't attach any label to it, thus implying that it is a part of normal, everyday English.
My impression is that kludge tends to show up in informal, conversational-style writing rather than in relatively formal writing. At the computer magazines where I worked for many years, kludge and kludgy appeared in articles fairly frequently, without anyone batting an eye. In a computing milieu, then, I think kludge is generally acceptable and very likely to be understood in the intended sense.