I've been searching for closing in on eight hours trying to find a source from a Karaite about who they think created the rabbinic Oral law. I heard someone claim that Karaites believe Moses created the Oral law but it was his own invention, not given to him by God. This sounded fishy to me, and while I can't find that claim anywhere, I also can't find any other culprit for the creation of the rabbinic tradition. Who do they pin the fabrication on?
Well, I have time now to gather together the sources.
As I said, the answer is, somewhat humorously, "machloket" (dispute), which just goes to show you that Karaites, in the end, are Jews like any other sort of Jew... :D
Here's what Rabbi Bernard Revel wrote on the matter in his book "The Karaite Halaka":
"The question of the origin of Karaism, its causes and early development is still awaiting solution...They have no tradition as to their origin, and their opinions are conflicting...(pg. 2)
Not all early Karaites claimed antiquity for their schism. This is evident from the reply of Salman b. Yeruham to Saadia's mention of their late origin (Pinsker, II, 19). Another contemporary of Saadia, Abu Jusuf Yakub al-Kirkisani...gives a date for what he calls the Rabbanite dissension: Jeroboam, to make permanent the power he had usurped and to prevent the Israelites owing allegiance to the house of David, divided the nation by sowing the seed of dissension, perverted the Law, and changed the calendar (I Kings 12, 32). The followers of Jeroboam in later times are called Rabbanites. Those who remained faithful to the original laws were the ancestors of the Karaites. This fanciful explanation found no credence, even among Karaites." (pg. 4)
That's one view - that the Oral Law was invented by King Yerov'am in order to ensure that the schism between the Kingdom of Judah and the Kingdom of Israel become permanent.
Note: Kirkisani's writings, like most writings of early Karaites, have not been translated into English from the original Arabic, hence my not quoting him directly.
"The Karaites felt keenly the need of some account of their origin that would silence the reproach of the Rabbanites and found in the event recorded in the Baraita (Kiddushin 66a; see Josephus Ant. XIII, 13, 5) a basis for claim of ancient origin for their sect. As stated in that narrative, the disagreement between John Hyrcanus and the teachers of the Law resulted in the extermination of the latter, excepting Simeon b. Shatah. As a consequence, ignorance of the Law prevailed until Simeon appeared and reinstated it.
"והיה העולם משתומם עד שבא שמעון בן שטח והחזיר התורה ליושנה" Simeon, say the Karaites, being at that time the sole authority, introduced many innovations upon his return and changed the true interpretation of the Law. To enforce these new laws, he invented the fiction that besides the Written there is also an Oral Law given to Moses on Sinai and handed down from generation to generation, and that the laws proclaimed by him went back to this real tradition.
The people followed him blindly. But some of them, knowing the false basis of these changes, rejected them and adhered to the ancient Tradition in all its purity; those were the Karaites." (pg. 5)
And that's the second view - that it was invented by Rabbi Shimon ben Shetach as part of a conspiracy to convince all of the Jews that these "new" laws had always been around.
See the footnotes for a list of Karaites who state this and quotes from their books.