"compromise your health" is correct and usable in written English. You can use this phrase to refer to a situation where taking an action may negatively influence one's health. For example: "If you don't get enough rest, you're compromising your health.".
Failing to get enough sleep night after night can compromise your health and may even shorten your life.
This could seriously compromise your health.
Unless it might actually cause bodily harm or compromise your health in some way, it's probably not as bad as your mind would have you think!
Continuing the fast may compromise your health.
In late 2014, the British Dietetic Association advised against the diet, arguing that it was a surefire way to compromise your bone health (given the complete bar on dairy intake) as well as helping you to miss out completely on several important nutrients.
Don't compromise your child's health by denying them vaccination.
However, this should really be a last resort, as resources at both of these public animal shelters are limited, and you will very likely compromise your dog's health and sanity.
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu