I currently have no health ins. coverage.
The health insurance from my new employer will not start for 90 days.
Do I need to get ins. for the 90 days?
If I do not purchase will there be a penalty since I will have ins. in about 80 days.
If you are going to miss more than two full months of coverage then you'll need other coverage during an employers 90 day waiting period.
Under the Affordable Care Act everyone is allowed less than three full months without coverage, or another exemption a year. This is due to a "short coverage gap" exemption.
If you have a 90 waiting period that will cause a gap longer than 3 months then consider either paying the fee or getting another plan in the meantime.
If you have coverage for even one day of a month you are considered covered for that month. So 80 days is fine, 90 days may even be fine during months with 30 and 31 days, but more than three actual full calendar months is not.