Babies can begin using high chairs when they're able to sit up on their own without assistance which can be as early as 5 months of age but may not happen until 6 months of age.
Usually though babies can sit in high chairs including the high chairs in restaurants by age 6 months.
Just make sure your baby is able to sit up on their own without any assistance before putting them in the high chair and always supervise the child while in the high chair even when they're strapped in.