Can I use Diancie's "Sparkling Wish" attack to evolve a Pokemon that I just put into play this turn?
Yes, you can do that.
Source: Burning Shadows FAQ (2017-07-20), TPCi Rules Team (2017-08-03)

Relevant cards

Note: All applicable cards may not be listed below.
SM3_94
SMA_SV36
SMA_SV36