Most value me above their brain
The radiation emitted from cellphones (or other electronic devices) cause brain damages yet we still use them.
or seek me for arms that are great
There are hair removal techniques that uses electromagnetic waves
Maxwell introduced me yet again
As did Ward, though a century late
In comments @Arcane explained it really well, so I am just copy/pasting it.
Maxwell gave the Classical theory of electromagnetism(1865) while Ward's Identity helped in Quantum ElectroDynamics in the 1950s(?)
One word and the cloud I will reach you
When you talk on phone, waves carrying the info transmits through air.
or help you get home on the ice
No idea. Maybe electromagnetic skates?
If I'm not being shot by the beach dudes
A reference to waves at sea/ocean.
I'll be playing with balls here at Rice
There is a belief that rice plant can absorb radiation(couldn't find the article so I wrote there is belief)
or maybe a reference to Rice University but other than random electromagnetic wave theory courses, couldn't managed to find connection.
p.s. since English is not my first language I probably missed some technical terms. If you know any, feel free to edit them in.