While there are various options in skincare and acne treatment available, natural essential oils are among the most popular to some degree.  They vary in their uses, and while some of them are more directly recognized for acne care than others, all of them have their individual virtues and uses for that matter. 
For example, jojoba oil is known to cleanse the scalp and hair, and it has been used as an effective moisturizer among other things for the skin without over-moisturizing or being oily in the process.  It has all the right components for success. Almond oil is also known as it is easily absorbed into the skin, to properly moisturize and provide you with the effective results you are looking for.  It is an excellent emollient.  Third, geranium oil has been known for its ability to bring a radiant glow tot the skin.  Lavender oil has been used as an antiseptic and as a stimulant, and finally rosemary oil has been known for its antioxidant properties.

However, among all these there is but one that has been directly connected to acne fighting.  Tea tree oil has been known for its antiseptic properties and even been tested in clinical studies against the popular and well known benzoyl peroxide, being shown to be just as effective without the side effects.  All these natural oils can have the effects you are looking for if you only try them.