Predictive processes and speech rhythm appear tightly interconnected during spoken language comprehension. Speech rhythm is often assumed to facilitate comprehension by shaping the time frame that influences neural entrainment and allows for temporal predictions to be formed. The present study asked the question about the relationship between linguistic predictability and rhythmic anticipation by using a rhythmic synchronization task. The task required participants to synchronize with the beat of spoken sentences repeated on a loop. The sentences differed in two sources of linguistic predictability, local (measured as surprisal of words within a sentence) and distal (implemented as repeating semantico-syntactic templates within a block of sentences). Thirty-two native speakers of British English took part in the study, tapping to the beat of sentences spoken in their native language. Signed asynchronies were measured from their synchronizations with nucleus onsets, to examine the degree of rhythmic anticipation. The results showed a greater degree of anticipation for the locally most informative parts of utterances within the distally most predictable context and could not be explained by bottom-up variability in acoustic salience (F0, duration, intensity). These findings suggest that the domain of predictively operating rhythmic attention in speech is linguistic rather than acoustic in nature.