Generally, no. Social Security's regular disability program, also known as SSDI, if paid for by contributions of workers. If a person get's SSDI and has children of the right age, those children may be eligible for benefits.
Technically, SSI is a welfare program. It is for people who are both low income and low assets. It does not have dependent benefits asociated with it.
However, there may be state programs. Also, if your child is an adult, there may be the possibility of disabled adult child disability benefits. And, if you are receiving retirement or disability benefits of your own, your child may be eligible. Finally, if your child is disabled and you are low income low assets, then perhaps your child will be eligible for SSI.
Of course, all of this depends on the specific facts or your child's situation and it could be wrong if facts are wrong or missing or different. Please see ssa.gov.
