Contrary to what one might think it actually seems that Hitler tried quite hard to keep Spain from joining his side during the Second World War. Throughout most of the War Franco was eager for both opportunistic and ideological reasons to join the Axis and made frequent overtures to Germany on that topic. However, both Hitler and German officials in general were less eager, for a variety of reasons, but most of them just come down to the reality that a friendly but non-belligerent Spain was far more useful than a new military ally would be.

A non-belligerent Spain provided crucial economic support for Germany, supplying them with tungsten and other key resources and even sending Spanish workers to help in German war industries. By contrast, to transform the Spanish military into an organization that could defend its own coasts let alone contribute substantially would have taken both time and significant industrial investment from Germany at a time when it had little. Hitler certainly did not want another Mussolini to deal with.

Hitler was quite open about this, complaining at length, for example, to the Italian foriegn minister about the Spanish State:

On 28 September, Hitler spoke with Ciano in Berlin, and he made no secret of his impatience with Franco, who promised a friendship that would be implemented only if Germany provided massive deliveries of grain, fuel and military equipment and granted Morocco and Oran. He preferred to leave the Vichy French to defend Morocco against the British. Hitler told Ciano that he opposed Spanish intervention ‘because it would cost more than it is worth’.Hitler had to balance the conflicting demands of Franco, Pétain and Mussolini, something which he conceded was possible only through ‘a grandiose fraud’.

• Preston, ‘Spain: Betting on a Nazi Victory’, p. 333

So to answer your question, Hitler did not try to get Spain to join the Axis during the War but had he, he probably would have succeeded at any time after the Fall of France in 1940 and before the Fall of Mussolini in 1943. However, even into 1944 Franco seems to have failed to have fully appreciated the situation the Axis found themselves in and it is impossible to say what a concerted diplomatic effort might have wrought.

 

Works Cited

Hernández-Sandoica, Elena, and Enrique Moradiellos, ‘Spain and the Second World War, 1939-1945’, in European Neutrals and Non-Belligerents During the Second World War, ed. by Neville Wylie, (Cambridge: Cambridge University Press, 2010), pp. 241–67

Preston, Paul, ‘Spain: Betting on a Nazi Victory’, in The Cambridge History of the Second World War, ed. by Joseph A. Maiolo and Richard J. B. Bosworth, III vols (Cambridge: Cambridge University Press, 2015), II: Politics and Ideology, pp. 324–48