Can you wear the Airborne tab on your shoulder even if you are not in an airborne unit?

I’d check the governing regulations on uniform wear. AR 670-1 & DA PAM 670-1. Once you’ve done a little research come back here and let us know what you think. Some of the questions on RP are very simple to answer on your own if you just take the time to do some searching around. Best of luck.

PRESIDENT'S HUNDRED TABS ARE THE
ONLY SPECIAL SKILL OR MARKSMANSHIP TABS AUTHORIZED FOR PERMANENT WEAR. THE
AIRBORNE TAB IS CONSIDERED AN INTEGRAL PART OF THE SHOULDER SLEEVE INSIGNIA
(SSI). AIRBORNE TABS ARE ONLY AUTHORIZED TO BE WORN ABOVE THE SSI IF
ASSIGNED TO ONE OF THE UNITS BELOW:
18TH AVIATION BRIGADE
82D AIRBORNE DIVISION
95TH CIVIL AFFAIRS BRIGADE
101ST AIRBORNE DIVISION
173D AIRBORNE BRIGADE COMBAT TEAM
360TH CIVIL AFFAIRS BRIGADE
528TH SUSTAINMENT BRIGADE
JOINT READINESS TRAINING CENTER OPERATIONS GROUP & HEADQUARTERS
SPECIAL FORCES GROUPS (AIRBORNE)
US ARMY CIVIL AFFAIRS & PSYCHOLOGICAL COMMAND
US ARMY ELEMENT, SPECIAL OPERATIONS COMMAND AFRICA
US ARMY ELEMENT, SPECIAL OPERATIONS COMMAND CENTRAL
US ARMY ELEMENT, SPECIAL OPERATIONS COMMAND EUROPE
US ARMY ELEMENT, SPECIAL OPERATIONS COMMAND KOREA
US ARMY ELEMENT, SPECIAL OPERATIONS COMMAND PACIFIC
US ARMY ELEMENT, SPECIAL OPERATIONS COMMAND SOUTH
US ARMY ELEMENT, SPECIAL OPERATIONS COMMAND, JOINT FORCES COMMAND
US ARMY ELEMENT, US SPECIAL OPERATIONS COMMAND
US ARMY JOHN F. KENNEDY SPECIAL WARFARE CENTER
US ARMY PARACHUTE TEAM
US ARMY SPECIAL OPERATIONS COMMAND
XVIII AIRBORNE CORPS
3. WEAR OF THE AIRBORNE TAB WITH ANY OTHER SSI IS NOT AUTHORIZED. REQUEST
COMMANDERS ENSURE THAT POLICY FOR WEAR IS ADHERED TO, AND ANY UNIT OR

No, the Airborne tab is a unit tab, not individual (which is why there is a separate Airborne badge--that one is for individuals who complete jump school). Unit tabs go with particular unit-shoulder-patches or SSI (Shoulder Sleeve Insignia), and you have to be in that particular unit to wear that particular patch. The caveat of course is the combat patch or SSI-FWTS (Shoulder Sleeve Insignia-Former War Time Service), which, if it is one of these Airborne units, you can wear on your right sleeve (with attached Airborne tab) even if not currently in an Airborne unit.