Can You Get Saints Row 1 on PS3? No—But Here's the Full Series on PlayStation

No. Saints Row (2006) launched on Xbox 360 and PC only. A PS2 port was cancelled. No PS3 version exists.

Saints Row on PlayStation

• Saints Row 2 (2008): PS3 / Xbox 360 / PC — best entry, still active mod community (Gentlemen of the Row on PC)
• Saints Row: The Third (2011): PS3 / Xbox 360 / PC — over-the-top, co-op
• Saints Row IV (2013): PS3 / Xbox 360 / PC — superpowers, aliens
• Saints Row: Gat out of Hell (2015): Standalone expansion, PS3/360/PC
• Saints Row (2022 Reboot): PS4/PS5/PC/Xbox — new cast, mixed reception

Start with Saints Row 2 (PS3) — deepest customization, best story, still holds up.