I have not been able to find firm evidence either way. The first issue to consider is what translations were available.
A French Jesuit missionary in Beijing, Father Amiot (Jean Joseph Marie Amiot, 1718-1793) was the first to translate Sun Tzu's work into a European language: Père Amiot, Art Militaire des Chinois, Paris: Didot L'Ainé 1772 (scan online). An English translation did not become available until the 20th century: Captain E. F. Calthrop (tr.), The Book of War, London: Murray 1908 (scan online).
The first German translation dates to 1910: Bruno Navarra (tr.), Das Buch vom Kriege, 80 pp., Berlin: Boll & Pickardt 1910. I have come across a reference to a Russian translation dating to 1860 but have not been able to find out any details. Given that Clausewitz died in 1831, the only translation potentially available to him was the French one.
The second issue to consider is what languages Clausewitz knew. During his lifetime French was by far the most common foreign language learned in Germany, in particular in aristocratic circles but also among the educated middle class. Next to his native German Clausewitz appears to have spoken French and English:
Christopher Bassford, "Clausewitz and His Works", Version 8 Mar 2016 (online)
In the Russian service, Clausewitz was somewhat hobbled by his ignorance of the Russian language. However, he spoke French (as well as English), as did many Russian aristocrats and the Russian imperial family, and there were many ethnic Germans in Russia and in the Russian forces.
Clausewitz spent some time in France as a prisoner of war, and from his comments on the French language and French theater in his correspondence it seems likely that he was fluent in the language:
Sibylle Scheipers, "Do not despair at your fate’: Carl von Clausewitz in French Captivity, 1806–1807," War in History, Vol. 28, No. 1, January 2021, pp. 5-24 (online):
He was detained in his role as adjutant to Prince August and as such shared the aristocratic privileges of captivity that the French granted to August. [...]
On 30 December 1806 August was sent into French captivity in Nancy, and Clausewitz accompanied him. [...]
Language would remain Clausewitz’s starting point in his observations about France and its society. He depicted the French language as affected and superficial: ‘If there has ever been a language that constrains the spirit like a close-fitting robe, it is French, and the French spirit in its stilted courtesy would be horrified by such a confession [referring to a confession of her love for Carl made by Marie in her previous letter, presumably] in spite of all the real hubris of the nation.’ From Paris, he wrote to Marie about the peculiarities of the French theatre. [...]
it was only the conclusion of the Tilsit Peace Treaty of 9 July 1807 that brought about August and Clausewitz’s release.
I conclude that Clausewitz could have read the French translation of Sun Tzu's work, but I have yet to find any evidence that he actually did so. A search and perusal of Vom Kriege (Berlin 1857, scan online) reveals no references to Sun Tzu specifically or even Chinese military strategy in general.