The simple answer is no. While HIV and AIDS are terrifying and carry a stigma about them, they are not as easily transmitted as people once thought. To better understand why many forms of interaction are safe while others carry a significantly higher risk factor, you need to understand the disease.
HIV and AIDS live in a person's bodily fluids but cannot survive for very long outside of the body on external surfaces. While saliva is a bodily fluid, it only contains a minute concentration of the virus. To pass the disease to someone else, they have to be exposed to a bodily fluid that contains enough of the virus either directly such as blood to blood contact or through mucous membranes.
The fluids that contain enough of the virus to infect another person are: blood, rectal fluids, seminal fluid and vaginal fluids. While these fluids can pass on the disease, it still would need to come into contact with a permeable surface on you to be transmitted. If you have cuts, scratches or other weaknesses in the skin, such as a rash, you do have a heightened risk factor but mucous membranes are the main issue.
Places such as the anus, cervix, the inner part of a man's foreskin, rectum, urethra, and vagina are the most common points of infection. While the mouth and throat can be points of infection, the mouth in particular does have a lower risk unless there are sores or poor oral hygiene at play.
While there has been one case where a person ended up with HIV due to kissing, there was blood involved along with very poor oral hygiene.
So, to recap, it is next to impossible to get HIV or AIDS from kissing someone unless there are circumstances that raise the risk factor.