How much and what sort of data do you need to store?
Certainly it is possible to add a Microchip 23K256 SPI SRAM to an Arduino Uno, but it is not cost effective because;
- you have to wire up the 23K256 chip to the Arduino, losing four pins that you can’t use for other purposes,
- you have to code and test access to the 23K256 chip; it isn’t a natural part of the ATmega328 processor or the Arduino environment,
- a fair bit of your 32KB Flash program memory and 2KB SRAM on the ATmega328 will be used up by the Arduino SPI interface library and your code to access the chip,
- you only gain 32KB of SRAM, and it is slow to access.
If price of the Uno is a concern, check out the KnockOffDuino at $6 (at present).
If I needed to store 256 Kbit (32 KB) in static RAM, I’d be choosing a processor with at least 64 KB of static RAM included. It would also depend on how quickly the data must be read or written. The Teensy LC has 62 KB of RAM and is about $24.