"arrogant smile" is a correct and usable phrase in written English.
You could use it in a sentence such as, "His arrogant smile belied his true feelings."
Indefatigably self-confident, cocky but not arrogant, flashing crinkling, boyish smiles and dancing around the stage like the boxer he used to be, Mr. Danza seems utterly at home with himself, his celebrity and having recently turned 50.
Mr. Harding was now smiling back with arrogant cunning, although with quite friendly, gentle manner.
Senator Rand Paul, Republican of Kentucky, told BuzzFeed, an online news site, that Mr. Biden looked like "an arrogant Cheshire cat with a big smile".
When Dan starred on Broadway in "How to Succeed in Business," he refused to smile during the curtain call, for fear of looking arrogant — it drove the producers crazy until he came around.
As a young man, studying politics at York university, people thought he was an arrogant git, "because I always wore a suit and never smiled".
The plump figure of Jayalalitha Jayaram, swathed in silken saris and smiling smugly in countless cartoons, has become a national caricature of the greedy, arrogant Indian politician.
"It looks arrogant, extremely arrogant.
