Due to the popularity of Old Fashioneds, which are often garnished with an orange peel, many bars have a surplus of peeled oranges/orange juice around. Orange juice is a bit watery and not as acidic as lemon or lime juice, so it doesn't have as much use in cocktails as other citrus. 

Some bars add isolated acids (citric, malic, tartaric) to orange juice to bring up its acidity closer to that of lemon/lime. Others merely find a way of using up a lot of orange juice. 

Of course, most bartender will know of the:

• Mimosa
• Screwdriver
• Blood and Sand

But here are some alternatives. 

Recipes that Use 1+ Ounces of Orange Juice

Garibaldi from Dante, NYC 

Recipes that Use .75 ounce (22ml) Orange Juice

What's Up, Doc?
From Laura Newman of Queen's Park, Birmingham

1 oz Svol Swedish Aquavit
1 oz carrot juice
.75 oz lemon juice
.75 oz honey syrup
.75 oz orange juice
.5 oz vodka
.25 oz orgeat
1 dash saline
1 dash absinthe
Whip shake with crushed ice; dump into a footed swizzle glass and top with more crushed ice
Garnish with a mint bouquet in the center of the glass (so it looks like a carrot)

Darryl Strawberry
From Laura Newman of Queen's Park, Birmingham

.75 oz strawberry-tarragon shrub
.75 oz orange juice
.75 oz simple syrup
.5 oz Seedlip Garden
1 dash saline
club soda, to top
Shake all ingredients (except soda) with ice; top with club soda and strain into an iced Collins glass
Garnish with half of a dehydrated orange wheel

"Duke's Julius" from Duke's Spirited Cocktails

"Our orange zest habit is countered with specialty happy hour recipes that call for orange juice, like our Duke’s Julius where the fresh juice meets gin, cream, vanilla bean, lemon, and our house saffron bitters." 

1.5 oz Oola Aloo Gin (great with rum too as many happy hour regulars have discovered)
.25 lemon
.5 oz half and half
1 oz orange cream syrup*

Shake and strain over pebble ice

*Orange Cream Syrup
1 quart orange juice
1/2 quart organic sugar
1/2 tahitian vanilla bean

Combine orange juice and sugar in a pot, and stir until dissolved. Cut the vanilla beans down the middle and add to the pot. Bring to a simmer, and let cook for 15 minutes. Add 1 oz Duke's Saffron Bitters [or a few threads of saffron added to the syrup as a substitute] and .5 oz lactart to each quart of finished syrup.