As I see it, drawing in Civics/Social Policies to military applications requires a redrawing of the so-called Promotions as well.
That's because right now, the 'promotions' are a combination of experience, tactical innovations, technical upgrades, weapons improvements, all jumbled together under an inappropriate title. Many of those could be instead invested in Civics.
For example.
Right now, Recon Promotions are:
Ranger - faster movement in woods and rainforest (tactical/terrain experience)
Alpine - faster movement on hills (tactical/terrain experience)
Sentry - can see through woods or rainforest
Guerrilla - can move after attacking (tactical/exerience innovation)
Spyglass - +1 sight range (technology upgrade - Renaissance Era to be exact)
Ambush - +20 Combat Strength in all situations (tactical innovation - but 'ambush' is practiced by Neolithic Hunters!)
Camouflage - only adjacent enemy units can see the unit (experience/technical upgrade - the term 'camouflage' applied to military units dates from 1916 CE)
And, worse, you can select a Ranger or Sentry Promotion without ever having had a Recon Unit move through a tile of woods or rainforest, or an Ambush Promotion without a Recon Unit ever getting into a battle with anyone. How are they learning this stuff?
instead, use Civics, representing experience in certain situations and innovation based on that experience:
Woodscraft (Ancient Era) - Faster movement in woods and rainforest
Bonus: X tiles of woods or rainforest tiles within your city radius (all cities combined)
Foresters (Medieval Era) - can see through woods and/or rainforest
Bonus: X tiles of woods or rainforest being Worked (all cities combined)
Lure of the High Country (Ancient Era) - faster movement on hills
Bonus: X tiles of hills and Mountains within your city radius (all cities combined) - Mountain tiles count double
Hit and Run (Classical Era) - can move after attacking
Bonus: X attacks by your Recon units on enemy military Units.
Spy Out the Land (Renaissance Era) - +1 sight range
Bonus: X times one of your Recon units ended a move next to an enemy military Unit
Ranger Training (Industrial Era) - +20 Combat Strength in all situations
Bonus: X times a Recon Unit kills an enemy combat Unit.
Silent and Deadly (Modern Era) - only adjacent enemy units can see the unit.
Bonus: X times a Recon Unit captured an enemy civilian Unit
'X' would have to be determined by playtesting, but it would be an increasingly large number, because once you 'get' one of these Civics, you can select them at any time: basically, you know how to train your Recon units in these techniques.
Promotions for units would be relegated to being able to do what they already do, only better - incremental increases in Combat Factor or Movement, not entirely new capabilities, as now.