Bummer bud. 360 years and wiped out by bureacratic action. Don't know of any that were older. Ranger is an English Language idea/unit. Might be others in other countries but they are relatively recent additions.
The oldest units in the US military obvoiusly have nothing on that.
The oldest US Marine unit is the 1st Marine Division and was activated 1 Feb 1941.
The oldest US Army unit is the 1st Infantry Division and was activated May 24, 1917.
The oldest US Army regiment is the 3rd Infantry Regiment and was activated June 3, 1784.
The oldest German Division that is active today is the 10th Panzer Division which was activated in 1915.
The German 1st Panzer Grenadier can trace its history back to the Grenadier-Regiment Kronprinz (1. Ostpreuß.) Nr 1 which was formed in 1655 which would make that 352 years but this is only a trace history.
The German militay was reorganized so many times and the old German military was made up of several individual states having there own militarys such as Prussia, Bavaria and so forth so you can not say this unit is this old.
The local regiment now reserves was formed in 1777 and was originally called Butlers Rangers they morphed into the Lincoln and Welland Regiment and is probably the oldest in Canada but the most Famous would probably be toss up between the RCR the Royal Canadian Regiment or the PPCLI Princess Patricias Canadian Light Infantry