sigh-roll 

The act of simultaneously rolling one's eyes while loudly expelling a stream of air from one's mouth to express frustration, or shocked amazement.

From sigh and eye roll; Alt spelling seye-roll

After Bert told Jim about his drunken adventures while in rehab, Jim sigh-rolled loudly and left.

sigh-roll by MVCatdaddy May 3, 2014

sighroll 

When you are so exasperated you cannot decide whether to sigh or roll your eyes.

His inane questions about homecoming left me with nothing to do but sighroll.

sighroll by Coll-dawg January 22, 2009

*sighroll* 

A word emoji for rolling one's eyes and sighing at the same time. *sighroll* is a wistful way to show exasperation or express being at a loss for words; similar to SMDH.

"The girl I like thinks she has a shot at Chris Pratt now that he and Anna Faris split up - *sighroll* "

*sighroll* by Seth Landers August 18, 2017

Sighroll 

When an annoyed surgeon rolls his eyes and sighs at the same time to convey his displeasure.

usually preceded by things like “I didn’t know you needed that.” Exasperated *sighroll*.

Sighroll by bouchard32 February 9, 2022