Can I use ISP header 01 cable to program 25LC640 SOIC8 in circuit?

Yes. For such 8 pin serial EPROM, you can select 25LC640 SOIC8 in the software.
And then use ISP Header-01 Adapter to connect the programmer and the chip on board. Only the lower 8 pins on ISP header are used. ISP adapter pin out in the instruction is shown as 10 pin DIP.

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