No. The U.S. government claims that annexation would violate international law and the Ukrainian constitution because Ukraine has not given its consent to the referendum. But Russia is not bound by the Ukrainian constitution. Nor does any international law prohibit two countries from merging together.
The real question is then whether Crimea’s secession–which you might think of as a legally separate act that (conceptually) precedes the annexation–violates international law. As I explained before, there is no law against one territory seceding from another. In fact, the right to self-determination is enshrined in the UN charter and several human rights treaties. Ukraine could certainly try to stop its territory from seceding–just as the United States fought to prevent the South from seceding–but if it fails, it can’t complain that the secession violates international law. Ukraine’s best argument is that the secession was driven by Russian meddling–Russia’s invasion of Crimea did violate international law, and the occupation violates Ukraine’s sovereignty. But if the referendum is free and fair, that argument will lose much of its force. Perhaps, Ukraine is owed some remedy by Russia (good luck), but that remedy could not be an injunction on Crimean secession, which would injure the Crimeans themselves.
U.S. officials note that Scotland’s secession vote was approved by the UK government. But the more pertinent analogy is Kosovo. Kosovo’s declaration of independence was not approved by the Serbian government. Kosovo’s secession was abetted quite significantly by the United States through military and diplomatic means.