While there is abundant experimental and theoretical work on polymer-induced DNA condensation, it is still unclear whether globular proteins can condense linear DNA or not. We develop a simple analytical approximation for the depletion attraction between rodlike segments of semiflexible polyelectrolytes such as DNA, induced by nonbinding globular proteins. Monte Carlo simulations show that the approximation works well up to protein volume fractions of at least 20%. From the expression for the depletion attraction we estimate instability thresholds by computing the effective virial coefficient of DNA segments in protein solutions. While globular proteins are found to be much poorer depletion agents than flexible polymers, it should be possible to condense linear DNA with small highly charged globular proteins, at relatively low ionic strengths.