In the United Kingdom, there are more than 1000 new cases of spinal cord injury (SCI) each year, with around half of these injuries affecting the cervical spine. People who have reduced function and control affecting their upper limbs may have difficulty carrying out activities of daily living (ADLs), significantly affecting their independence. Recovering even partial upper limb function is a top priority among tetraplegics. Regaining voluntary function in the upper limb can have a huge impact on quality of life. Using TSCS in the upper limb for acute SCI can benefit patients early in their rehabilitation, and may reduce the number of patients with problematic spasticity at discharge. Transcutaneous spinal cord stimulation (TSCS) may provide a low-cost method of improving function and spasticity in this cohort. The aim of this feasibility study is to assess and compare the impact of adding TSCS to the standard rehabilitation of inpatients with acute SCI, compared to a sham (placebo) TSCS intervention added to standard rehabilitation, in an effort to enhance upper limb control and function.