No. Romanian is a Romance language in the Italic branch of the Indo-European family—the same broad group as Italian, Spanish, French, and Portuguese—not a Slavic language.
It developed from Latin spoken in the Carpathian–Danube region after Roman rule, and it is often described as Balkan or Eastern Romance because it evolved in eastern Europe. Centuries of contact with neighboring Slavic languages left vocabulary and some structural traces, but its core grammar and much of its lexicon remain Latin-based.
Source: UCLA Department of Slavic, East European & Eurasian Languages & Cultures — Romanian background.