  We study the properties of the leading Regge trajectory in open string theory
including the open string planar one-loop corrections. With SU(N) Chan-Paton
factors, the sum over planar open string multi-loop diagrams describes the 't
Hooft limit N\to\infty. Our motivation is to improve the understanding of open
string theory at finite \alpha' as a model of gauge theories. SU(N) gauge
theories in D space-time dimensions are described by requiring open strings to
end on a stack of N Dp-branes of space-time dimension D=p+1. The large N
leading trajectory \alpha(t)=1+\alpha' t+\Sigma(t) can be extracted, through
order g^2, from the s\to-\infty limit, at fixed t, of the four open string tree
and planar loop diagrams. We analyze the t\to0 behavior with the result that
\Sigma(t)\sim-Cg^2(-\alpha' t)^{(D-4)/2}/(D-4). This result precisely tracks
the 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. In
particular, for D\to4 it reproduces the known infrared divergences of gauge
theory in 4 dimensions with a Regge trajectory behaving as -\ln(-\alpha^\prime
t). We also study \Sigma(t) in the limit t\to-\infty and show that, when D<8,
it behaves as \alpha^\prime t/(\ln(-\alpha^\prime t))^{\gamma}, where \gamma>0
depends on D and the number of massless scalars. Thus, as long as 4<D<8, the
1-loop correction stays small relative to the tree trajectory for the whole
range -\infty<t<0. Finally we present the results of numerical calculations of
\Sigma(t) for all negative t.
