As a general reference, I’d suggest taking a look at the Catalyst symbolic reaction systems tutorial.
For your specific question, you can do it in two ways. In the approach you are taking you need to declare, a,b,c,T as parameters and A,B,C as variables like
@parameters a b c T
@variables t A(t) B(t) C(t)
rxns = []
push!(rxns, Reaction(arrhenius(a, b, c, T), [A, B], [C]))
@named arrhenius_sys = ReactionSystem(rxns, t)
Alternatively, Catalyst also has a macro that works on a reaction level
rx = @reaction arrhenius(a, b, c, T), A + B --> C
rxns = [rx]
@variables t
@named arrhenius_sys = ReactionSystem(rxns, t)