Technician reported striking the fuselage of the aircraft with an oil cart during routine engine service. The aircraft was removed from service for repairs.

Narrative

I went to the gate to service Aircraft X due to its late arrival; which meant I needed to service my own engine oils; which is normally done by the terminal guys; so I went to look for an oil cart. One cart was tagged out of service; the second cart was not charged properly; so could not use it. The cart I did find was at [Gate] XXX being used by another crew. They agreed to let me use the cart once they were finished. The aircraft had just arrived shortly and was being offloaded and serviced by our guys and others. I went to get the cart; which was located on the inbound side of the right engine. As I drove away because the hydraulics were on above; I scraped the bottom of the fuselage with the bar on top of the oil cart; then immediately stopped. Seeing the damage; I immediately contacted Person A; Terminal XX; of what had happened. Person A then contacted the Manager on Duty.I believe it happened because I was multitasking; the loud noises; sharing the space with Ramp and other maintenance crew/equipment; and my rush to complete this task in a timely fashion; along with having to wait to borrow the only working piece of equipment. We should not drive the oil cart so close to plane without a guide person; not to rush when servicing aircraft; be more aware of my surroundings; especially under construction conditions; more control maneuvering when around other vehicles on the ramp; focus more on task in the presence of loud noises; [and] pay attention to the variations of the equipment and their dimensions.