As you have asked about the list of Army Careers in United States of America (USA), I am giving you information about it, check below for the details

Infantry Branch (IN)
Corps of Engineers Branch (EN)
Field Artillery Branch (FA)
Air Defense Artillery Branch (ADA)
Aviation Branch (AV)
Cyber Branch (CY)
Special Forces Branch (SF)
Armor Branch (AR)
Telecommunications Systems Engineering Functional Area (FA )
Signal Corps Branch (SC)
Judge Advocate General Branch (JA)
Electronic Warfare Functional Area (FA )
Information Operations Functional Area (FA )
Military Police Branch (MP)
Strategic Intelligence Functional Area (FA )
Military Intelligence Branch (MI)
Financial Management Branch (FI)
Psychological Operations Branch (PO)
Civil Affairs Branch (CA)
Space Operations Functional Area (FA )
Adjutant General Branch (AG)
Public Affairs Functional Area (FA and CMF )
Academy Professor Functional Area (FA )
Foreign Area Officer Functional Area (FA )
Operations Research/Systems Analysis Functional Area (ORSA) (FA )
Force Management Functional Area (FA )
Army Acquisition Corps (FA and CMF )
Systems Automation Officer Functional Area (FA )
Simulation Operations Functional Area (FA )
Chaplain Branch (CH)
Strategic Plans and Policy Functional Area (FA )

Medical Department Branches
. Medical Corps Branch (MC)
. Dental Corps Branch (DC)
. Veterinary Corps Branch (VC)
. Medical Specialist Corps Branch (SP)
. Nurse Corps Branch (AN)
. Medical Service Corps Branch (MS)
. Medical CMF
. Health Services FA
. Laboratory Sciences FA
. Preventive Medicine Sciences FA
. Behavioral Sciences FA

Chemical Branch (CM)

Logistics Corps
. Transportation Branch (TC)
. Ammunition CMF, Mechanical Maintenance CMF & Ordnance Branch (OD)
. Quartermaster Corps Branch (QM)