Question: Is it common to denote a chord symbol with an arpeggio marking? How else would you indicate that the chord is to be played arpeggio?

Answer: 
For piano music it is common to mark the chord with one of the usual signs. (Look up the other answers.) 

But in simple chord accompaniments for guitar in folk - 
and pop music it is up to the interpret if he wants to play arpeggio or a strummed chord. This means: There is not a common sign.

(I didn’t understand the question in the sense that you were asking as a songwriter or composer how you could mark a arpeggio for the players.)
Another commenter explained the arpeggio symbols used in staff notation, but your question is about **chord symbols.**

The principle behind the chord symbols used in jazz and pop music is to let the instrumentalist follow their own intuition in choosing voicings and textures. If there is a specific arpeggiated pattern you want, it's best to simply write it out note by note, or write out one bar of example notation and then write the word *simile* over the subsequent measures.

If you don't have a particular arpeggiated pattern in mind, you can simply write the word *arpeggio* near the chord symbol. Any literate musician will understand this to mean that they should improvise their own arpeggiated pattern.

When you'd like them to stop arpeggiating, you can use the word *comp* in jazz, or simply *end arpeggio* or something to that effect.

Another option is to refer to a specific style of arpeggiation, like *montuno, Coldplay,* or *in the style of John Lennon's "Imagine."* A pianist experienced with reading jazz and pop charts will know what these things mean.

My larger point is that if there is an accompanying technique that you feel you can describe better in words than in notation, then you should simply **use words.** Many beginning composers feel pressured to use the "proper" Italian terms and musical symbols to communicate their ideas, but it has long been a staple of notational practice for composers to add instructions in their native languages.