The Vienna Atomic Line Database (VALD) is a comprehensive database of atomic and molecular transition lines. It contains over 50 million lines for over 100,000 atoms and molecules.

The National Institute of Standards and Technology ASD (The NIST ASD) is a database of atomic and molecular spectral data. It contains over 10 million lines for over 80,000 atoms and molecules.

If the database contains lines that match the molecule's signature, then you will be able to identify the molecule in the spectrum.