My recommendation for a system that would play the game would be any system meeting or exceeding these requirements. I generally build my own systems, so have little knowledge of what pre-built systems are currently available. Just match any system you're looking at to these specs, and you'll be able to play with recommended settings.
Might be best off looking for an older, used gaming rig. The requirements really don't look too steep, and a gaming rig from 2011 - 12 might be able to meet the requirements without costing you a small fortune.
On the other hand, if you're wanting new, the higher tiered of the two brand new CPUs from AMD, the Ryzen 5 2400G with Radeon RX Vega 11 Graphics, may be able to fit a budget build and give you good enough performance. The real downside is the DDR 4 is going to cost far more than it's worth, and is required to use one of the new CPUs.
Tom Clancy's Rainbow Six: Siege Recommended Requirements
CPU: Intel Core i5-2500K @ 3.3GHz or better, AMD FX-8120 Eight-Core @ 2.6Ghz or better
RAM: 8 GB
OS: Windows 7 64 bit, Windows 8 64 bit, Windows 10 64 bit
VIDEO CARD: NVIDIA GeForce GTX 670 or AMD Radeon HD 7970 / R9 280x (2GB VRAM)
SOUND CARD: Yes
FREE DISK SPACE: 47 GB