Sensorimotor synchronization as a means of studying rhythmic perception-action coupling has been extensively researched across a large number of temporally regular structures including music while little is known about synchronization with speech. The present study fills this gap by applying a sensorimotor synchronization paradigm to natural speech and studying acoustic landmarks that may serve as perceptual anchors of rhythmic movement in spoken sentences. Five rhythmically relevant types of acoustic landmarks were identified in twenty sentences of English containing syllables with vocalic and non-vocalic nuclei. The landmarks were either manually defined or algorithm-generated and included nucleus onsets, peaks and onsets of inter-syllabic and inter-stress timescales, moments of the fastest energy change (approximating the P-center location), and timepoints of combined pitch and periodic power. Sensorimotor synchronization data from 32 native English participants were examined with regards to the location of an increased synchronization activity in the proximity of the predefined landmarks. The results demonstrated that participants synchronized with syllable-size units regardless of the type of syllable nucleus (vowel or consonant) and that their taps were consistently timed close to nucleus onsets. Hereby, the manually defined nucleus onsets predicted synchronization peaks as well as the algorithm-generated moments of the fastest energy change around nucleus onsets (i.e., a model of the P-center location) did. In contrast, other landmarks did not constitute a stable acoustic anchor of sensorimotor synchronization with English speech. The synchronization performance was not influenced by either acoustic F0-information or by phonological tune specifications. These findings provide new evidence for the proposals that rhythmic attention in natural speech may be locked on to fast spectral changes within a syllable as the smallest structuring unit of prosodic hierarchy.