Mobile phone has become a basic necessity in our daily life. With more than 7 billion mobile phone users worldwide, the prevalence of smartphones has led to an increase in applications for health monitoring. This paper suggests an autocorrelation-based technique for predicting Heart Rate (HR) from single-axis accelerometer data, utilizing the integrated motion sensor for acceleration in mobile phones. To extract the cardiac signal, the proposed method employs a combination of Butterworth and Bessel filters to preprocess the accelerometer data and isolate periodic segments corresponding to heartbeats. A dataset of simultaneous accelerometer and ECG from 300 individuals with Atrial Fibrillation (AF) and Sinus Rhythum (SR) were used to evaluate the technique. The HR is measured by comparing the difference between the first two peaks in valid segments of each subject. For subjects in SR, the method demonstrated high accuracy with a Mean Absolute Error (MAE) of 4.54 Beats per Minute (BPM), aligning with clinical accuracy standards. However, a higher MAE of 15.7 BPM was observed in AF subjects, highlighting the need for further refinement in arrhythmic populations. Future research will focus on enhancing accuracy across diverse cardiac conditions and expanding validation across larger and more diverse datasets.