No, he wasn't. Frederick the Great was king of Prussia.
Well, that also depends on how picky you are!! I'm not an expert on the following, so somebody maybe should correct me, but this shows what 18th century politics was like .......
The Hohenzollern holdings by the 17th century included their power base, as the Elector of Brandenberg, which held the title of Margrave, and of the ruler of the Dukedom of Prussia.
Frederick the Great's Grandfather, Frederick I (I think he had a different title as Elector of Brandenberg, maybe Frederick III?) was needling to become a 'king'. Under the treaty of the Holy Roman Empire, the only kingdom allowed in the empire was Bohemia, and only the Emperor, who at the time was Leopold I of Habsburg, could give him the title.
Leopold wanted Frederick I's help against France in the War of Spanish Succession, so he allowed a compromise. Frederick could be a King IN Prussia. That is, since Prussia was not part of the Holy Roman Empire, Leopold agreed that Frederick could call himself King in Prussia, and that was his title, but not in Brandenberg. He was NOT 'King OF Prussia'!
Of course, Frederick I went around calling himself 'King in Prussia' and not as often 'Elector of Brandenberg'. (Similarly, Frederick the Great's enemy, Maria Theresa, called herself 'Queen', since she was Queen of Hungary but she was Archduchess of Austria).
Frederick I son, Frederick the Great's father, was Frederick William I, who also called himself 'King in Prussia'.
Frederick the Great, when he took over in 1940, stopped the pretense and started calling himself 'King of Prussia' (not sure exactly when). So, yes, I guess we can say that he was the 'King of Prussia', but, of course, scholars often point out that it wasn't technically correct. But, we are talking about Frederick the Great, who was going to stop him?
Anyway, this shows that modern day lawyers could have had a field day in previous times. Could you imagine how many people would be arguing about this if it happened today!
Best wishes,
Bruenor