34 years have passed since Voyager I took off and it's just crossing the solar system, being approximately at 16.4 light-hours away. How much time have passed for itself, though?
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Using those numbers, let's assume it has been traveling in a straight line at constant speed.1 Then the speed is $$ v = \frac{16.4~\mathrm{hr}\cdot c}{34~\mathrm{yr}} = 5.5\times10^{-5} c, $$ so we can see right away it is traveling at a negligible fraction of the speed of light.
Still, we can compute the effects of time dilation. The relevant factor is $$ \frac{1}{\gamma} = \sqrt{1 - \frac{v^2}{c^2}} = 1 - 1.5\times10^{-9}. $$ This is because the proper time experienced by the spacecraft is the time lapse we experience - call it $\Delta t_\text{Earth}$ - divided by gamma: $$ \Delta t_\text{Voyager} = \frac{1}{\gamma} \Delta t_\text{Earth}. $$ The spacecraft's clocks have progressed just a hair under $34$ years - in fact, they are slow by $$ 1.5\times10^{-9} (34~\mathrm{yr}) = 1.6~\mathrm{s}. $$
1 This is not quite true, but the general result is still the same.