Sea turtles are generally slow swimmers traveling at a speed of 2.8 to 10 km/h (1.7 to 6.2 mp/h) with slight variation between the species.
The leatherback sea turtle has been recorded swimming as fast as 35 km/h (22 mph), according to the San Diego Zoo. This speed is usually just achieved during brief bursts, for example due to flight reactions.
References:
Eckert SA 2002. Swim speed and movement patterns of gravid leatherback sea turtles (Dermochelys coriacea) at St Croix, US Virgin Islands. Journal of Experimental Biology 205: 3689-3697. Papi F, Luschi P, Croisio E and Hughes GR 1997. Satellite tracking experiments on the navigational ability and migratory behaviour of the loggerhead turtle Caretta caretta. Marine Biology 129: 215-220.