If you have the symbolic math toolbox, then you should be able to follow the instructions in Chapter 3 here.
I tried to do this for your example:
syms t tau
a = 10;
omega = 2*pi*100;
f = a*exp(-a^2/(4.0*t))/(2.0*sqrt(pi)*t^(3.0/2.0));
g = exp(1i*omega*t);
z = int(subs(f,tau)*subs(g,t-tau),tau,-inf,inf);
z = simplify(z);
but the ...
That depends on what you want to plot: The response of the continuous time system or the response of a sampled discrete time system, which will always depend on the choice of sample rate.
Your system is not band-limited, so it can't be sampled without some amount of aliasing.
Do I just evaluate s at iω
If you just want to look at the approximate frequency ...