Yes, but every free tier has a wall and it's worth knowing where. Zoho People's free plan is the most complete: a real HRIS with employee records, leave management and self-service for up to five users, no credit card. Homebase's free tier covers one location and does the job properly if your team clocks in and out.
The catch is what happens when you outgrow it. Zoho's paid pricing is geo-split and the gap is large — Essential HR is $1.50 per user per month globally but $4 in the US — and performance management is not in the cheapest tier, despite what several comparison sites claim.