Can a Reform Jew believe the Torah is the word of God?
In answer to your question, "Can a Reform Jew believe that God gave the Torah at Sinai?" I think that the most honest answer is, "Yes, but..." Let me start with that "but.
Why Do We Observe Shavuot by Studying All Night?
Since the Rabbinic period, Shavuot has been tied to the story of the Israelites receiving the Torah at Sinai. Because of this, Shavuot has come to be dedicated to the idea of Torah study and Jewish education.
Stories We Tell: Hero Israel
On the Other Hand: Ten Minutes of Torah – T'rumah: Building a Sacred Space
Parashat T'ruma describes building a mishkan, a sacred space, and the first central praying place in Jewish life. People were asked to give both their skills and their material possessions to build it, and together they created something both beautiful and portable.