This paper investigates the problem of secret key generation from correlated Gaussian random variables in the short block-length regime. Inspired by the state-of-the-art performance provided by polar codes in the short blocklength regime for channel coding, we propose an explicit protocol based on polar codes for generating the secret keys. This protocol differs from previously proposed key generation protocols based on polar coding in two main ways: (i) we consider a Gaussian source for the key generation; (ii) we focus on the short block-length regime. Simulation results show that the proposed protocol performs well even for very short blocklengths, especially if one can relax the BER requirements for the generated keys. They also demonstrate that the polar code based protocol outperforms a similar one using LDPC codes in place of polar codes, and that this advantage grows the shorter the blocklength becomes.