The three charges were reckless driving causing death, failing to help a victim after a crash and cocaine abuse.
Pol Capt Pichapai Srikhamkhwan, deputy investigation chief at Thong Lor police station, on Tuesday asked the court to issue the warrant for the arrest of Mr Vorayuth based on new evidence - testimony given by experts and examination of cocaine use, Thai media reported.
The arrest warrant for this has a statute of limitations for 15 years.
Earlier, a deputy attorney-general and an acting police chief decided not to arraign him on the charge of reckless driving causing death.
The decision sparked a public outcry and led to a reinvestigation into the case.
Mr Vorayuth, 35, also known as Boss, was wanted on manslaughter charges over the hit-and-run death of Pol Snr Sg Maj Wichian Klanprasert, 47, in the early morning of Sept 3, 2012
He delayed hearing charges seven times. It was not until April 27, 2017, that prosecutors finally charged him with reckless driving causing death and failing to help a crash victim.
He fled on a private plane two days before he was due to face the charges.