Physically Unclonable Functions (PUFs) have become an important and promising hardware primitive for device fingerprinting, device identification, or key storage. Intrinsic PUFs leverage components already found in existing devices, unlike extrinsic silicon PUFs, which are based on customized circuits that involve modification of hardware. In this work, we present a new type of a memory-based intrinsic PUF, which leverages the Rowhammer effect in DRAM modules; the Rowhammer PUF. Our PUF makes use of bit flips, which occur in DRAM cells due to rapid and repeated access of DRAM rows. Prior research has mainly focused on Rowhammer attacks, where the Rowhammer effect is used to illegitimately alter data stored in memory, e.g., to change page table entries or enable privilege escalation attacks. Meanwhile, this is the first work to use the Rowhammer effect in a positive context: to design a novel PUF. We extensively evaluate the Rowhammer PUF using commercial, off-the-shelf devices, not relying on custom hardware or an FPGA-based setup. The evaluation shows that the Rowhammer PUF holds required properties needed for the envisioned security applications, and could be deployed today.